wssv - white spot syndrome virus · 2015-05-13 · wssv - white spot syndrome virus. rcn marine...
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WSSV - White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Digestive tract Ventral Nerve chord
Circulatory system Respiratory system
Hematopoietic tissueLymphoid organ
Female reproductive tract Male reproductive tract
Decapod anatomy
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
210-380nm
70-167nm
Envelope
Envelope proteins
Envelope extension
Nucleocapsid
Genome
Tegument
bull dsDNA - ~300kbpbull 185 ORFs
bull Baculoviralesbull Nimaviridae
bull Whispovirus
WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
ldquoBaculoviralesrdquoNimaviruses
HystrosavirusesGpSGHV
MdGHV
WSSV
CunNPV
NeleNPV
AcMNPV
CpGV
HzNV-1
PmNV
GbNV
OrNV
CcBV
TnZBV
CiBV
Bracoviruses
Nudiviruses
Baculoviruses
Wang Y Jehle JA 2009 JIP 101 187-193 Wang Y et al 2011 Vir Gen 42444 ndash 456 Theacutezeacute J et al 2011 PNAS 10815931-35
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
1950 1970 1990 2010
75
25
Poun
ds (x
109 )
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp commodity production
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon
Marsupenaeus japonicusFenneropenaeus chinensis
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
050
100150200250300350400450500
1980 1985 1990 1995
Year
Mill
ions
of P
ound
s
Production of Farmed Shrimp - China
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
19921994 1994 1998
1996
19932002
200219971995
1999
19991999
1999
2005
Spread of WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Emergence of White spot syndrome virus
1 km
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Digestive tract Ventral Nerve chord
Circulatory system Respiratory system
Hematopoietic tissueLymphoid organ
Female reproductive tract Male reproductive tract
Decapod anatomy
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
210-380nm
70-167nm
Envelope
Envelope proteins
Envelope extension
Nucleocapsid
Genome
Tegument
bull dsDNA - ~300kbpbull 185 ORFs
bull Baculoviralesbull Nimaviridae
bull Whispovirus
WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
ldquoBaculoviralesrdquoNimaviruses
HystrosavirusesGpSGHV
MdGHV
WSSV
CunNPV
NeleNPV
AcMNPV
CpGV
HzNV-1
PmNV
GbNV
OrNV
CcBV
TnZBV
CiBV
Bracoviruses
Nudiviruses
Baculoviruses
Wang Y Jehle JA 2009 JIP 101 187-193 Wang Y et al 2011 Vir Gen 42444 ndash 456 Theacutezeacute J et al 2011 PNAS 10815931-35
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
1950 1970 1990 2010
75
25
Poun
ds (x
109 )
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp commodity production
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon
Marsupenaeus japonicusFenneropenaeus chinensis
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
050
100150200250300350400450500
1980 1985 1990 1995
Year
Mill
ions
of P
ound
s
Production of Farmed Shrimp - China
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
19921994 1994 1998
1996
19932002
200219971995
1999
19991999
1999
2005
Spread of WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Emergence of White spot syndrome virus
1 km
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
210-380nm
70-167nm
Envelope
Envelope proteins
Envelope extension
Nucleocapsid
Genome
Tegument
bull dsDNA - ~300kbpbull 185 ORFs
bull Baculoviralesbull Nimaviridae
bull Whispovirus
WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
ldquoBaculoviralesrdquoNimaviruses
HystrosavirusesGpSGHV
MdGHV
WSSV
CunNPV
NeleNPV
AcMNPV
CpGV
HzNV-1
PmNV
GbNV
OrNV
CcBV
TnZBV
CiBV
Bracoviruses
Nudiviruses
Baculoviruses
Wang Y Jehle JA 2009 JIP 101 187-193 Wang Y et al 2011 Vir Gen 42444 ndash 456 Theacutezeacute J et al 2011 PNAS 10815931-35
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
1950 1970 1990 2010
75
25
Poun
ds (x
109 )
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp commodity production
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon
Marsupenaeus japonicusFenneropenaeus chinensis
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
050
100150200250300350400450500
1980 1985 1990 1995
Year
Mill
ions
of P
ound
s
Production of Farmed Shrimp - China
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
19921994 1994 1998
1996
19932002
200219971995
1999
19991999
1999
2005
Spread of WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Emergence of White spot syndrome virus
1 km
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
ldquoBaculoviralesrdquoNimaviruses
HystrosavirusesGpSGHV
MdGHV
WSSV
CunNPV
NeleNPV
AcMNPV
CpGV
HzNV-1
PmNV
GbNV
OrNV
CcBV
TnZBV
CiBV
Bracoviruses
Nudiviruses
Baculoviruses
Wang Y Jehle JA 2009 JIP 101 187-193 Wang Y et al 2011 Vir Gen 42444 ndash 456 Theacutezeacute J et al 2011 PNAS 10815931-35
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
1950 1970 1990 2010
75
25
Poun
ds (x
109 )
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp commodity production
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon
Marsupenaeus japonicusFenneropenaeus chinensis
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
050
100150200250300350400450500
1980 1985 1990 1995
Year
Mill
ions
of P
ound
s
Production of Farmed Shrimp - China
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
19921994 1994 1998
1996
19932002
200219971995
1999
19991999
1999
2005
Spread of WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Emergence of White spot syndrome virus
1 km
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
1950 1970 1990 2010
75
25
Poun
ds (x
109 )
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp commodity production
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon
Marsupenaeus japonicusFenneropenaeus chinensis
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
050
100150200250300350400450500
1980 1985 1990 1995
Year
Mill
ions
of P
ound
s
Production of Farmed Shrimp - China
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
19921994 1994 1998
1996
19932002
200219971995
1999
19991999
1999
2005
Spread of WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Emergence of White spot syndrome virus
1 km
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Shrimp commodity production
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon
Marsupenaeus japonicusFenneropenaeus chinensis
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
050
100150200250300350400450500
1980 1985 1990 1995
Year
Mill
ions
of P
ound
s
Production of Farmed Shrimp - China
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
19921994 1994 1998
1996
19932002
200219971995
1999
19991999
1999
2005
Spread of WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Emergence of White spot syndrome virus
1 km
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Shrimp Aquaculture SpeciesLitopenaeus vannamei Penaeus monodon
Marsupenaeus japonicusFenneropenaeus chinensis
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
050
100150200250300350400450500
1980 1985 1990 1995
Year
Mill
ions
of P
ound
s
Production of Farmed Shrimp - China
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
19921994 1994 1998
1996
19932002
200219971995
1999
19991999
1999
2005
Spread of WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Emergence of White spot syndrome virus
1 km
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
050
100150200250300350400450500
1980 1985 1990 1995
Year
Mill
ions
of P
ound
s
Production of Farmed Shrimp - China
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
19921994 1994 1998
1996
19932002
200219971995
1999
19991999
1999
2005
Spread of WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Emergence of White spot syndrome virus
1 km
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
19921994 1994 1998
1996
19932002
200219971995
1999
19991999
1999
2005
Spread of WSSV
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Emergence of White spot syndrome virus
1 km
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Emergence of White spot syndrome virus
1 km
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
1 Environment changes bringing new contactsMore shrimpPonds built in new areas ndash where shrimp never were or in low numbersMore contact between other (terrestrial) arthropods and shrimp
2 Change in pathogen virulence
3 Introduced from elsewhere
Emergence of White spot syndrome virus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Source FAO
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
Worlds Production of Penaeid Shrimp
AquacultureCaptureTotal
0
5
10
15
Poun
ds (x
109 )
1950 1970 1990 2010
75
25
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
More shrimp ndash more placesGreater opportunity for contact between shrimp and other arthropods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Hosts of WSSV bull Shrimp
ndash Penaeusbull monodonbull semisulcatus
ndash Farfantepenaeusbull aztecusbull duorarum
ndash Fenneropenaeusbull chinensisbull indicusbull merguensisbull penicillatus
ndash Marsupenaeusbull japonicus
ndash Litopenaeusbull vannameibull stylirostrisbull setiferus
ndash Metapenaeus ensis
ndash Exopalaemonbull orientalis
ndash Macrobrachium sppndash Palaemon styliferuusndash Palaemonetes pugio
bull Crabndash Calappa lophosndash Charybdis
bull feriatabull natotor
ndash Helice spndash Portunus
bull pelagicusbull Sanguineolentus
ndash Callinectes sapidus
ndash Armasus cinereumndash Scylla serratandash Sesarma sppndash Sommanniathelpusa spndash Thalamita spndash Uca sppndash Menippe adina
bull Lobsterndash Panuluris
bull longipesbull ornatusbull argus
bull Crayfishndash Procambarus clarkiindash Cherax quadricarinatus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
0
100
200
300
400
500
600
700
800
900
1000
0 3 6 9 12 15 18 21
Num
ber o
f shr
imp
Day
Weight 3 gDensity 550m3
Dose 003 bwfinal survival 000 003max daily mortality 10 06
WSSV Litopenaeus vannamei
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Armasus cinereum
Uca panacea
Callinectes sapidus
Litopenaeus setiferus
Uca speciosa
Local decapods exposed to WSSV (China)
0 5 10 15 20 25 30Day
00
01
02
03
04
05
06
07
08
09
10
Surv
ival
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Salt marshes
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Mississippi sound
Jourdan
Biloxi
Pearl
Wolf
Lake Pontchartrain
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Prevalence of WSSV in decapods of Ms Sound
Blue crab (Callinectes sapidus) (83 n=12)
Purple marsh crab (Sesarma reticulatum) (100 n=20)
Gulf mud fiddler crab (Uca longisignalis) (500 n=72)
Panacea sand fiddler crab (U panacea) (108 n=1404)
Mudflat fiddler crab (U rapax) (230 n=88)
Spined fiddler crab (U spinicarpa) (357 n=98)
Red-jointed fiddler crab (U minax) (227 n=22)
Squareback marsh crab (Armasus cinereum) (267 n=30)
Daggerblade grass shrimp (Palaemonetes pugio) (94 n=1244)
White shrimp (Litopenaeus setiferus) (200 n=40)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Modeling WSSV in communities of decapods
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
WSSV life cycle diagram
λ Host recruitmentβ TransmissionLiveχ TransmissionDeadα MortalityWSSVμ MortalityNaturalδ DecayCarcassη ConsumptionCarcass
δ η
Susceptible Infected Dead
β
χ
λ
micro
α micro
( ) ( )( )( ) ( )( ) ( ) ( )( )
( ) ( )( ) ( ) ( )( )
1
1
1
1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ λ micro
β χ α micro
α micro η δ
+
+
+
= minus sdot minus minus minus + minus
= + sdot minus minus minus minus minus minus sdot minus sdot
= + minus minus sdot minus sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
Transmission terms - Force of infection λprobability of infection after contact
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
( )1 1 Iλ β= minus minus
( )Iλ β= sdot
Force of InfectionProbability of infection after contact with all infecteds
Ross
Reed-Frost
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
1 2 3 4 5 6 7
1 11 12 13 14 15 16 17
2 21 22 23 24 25 26 27
3 31 32 33 34 35 36 37
S S S S S S S
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
I SI SI SI SI SI SI SI
( )1-
t t t tS S S Iβ
+= sdot sdot
RossKermack-McKendrick
If β is probability of transmission after one S contacts one IThen SI is number of contacts between every S and every I
May have more infects than susceptiblesSome transmissions are to the same susceptible
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
2(1 )βminus
1 βminusβ 1 βminusβ
21 (1 )βminus minus
3 Ways to become infected1 amp not 2 βlowast(1minusβ)ornot 1 amp 2 (1minusβ)lowastβor1 amp 2 βlowastβ
Only 1 way to remain uninfected1 amp 2 (1- β)lowast(1minusβ)
βlowast(1minusβ) + (1minusβ)lowastβ + βlowastβ
1- (1 )(1 ) t
t t tIS S S β+
= sdot minus minusReed-Frost
Black-Singer
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Epidemic models ndash parameter estimates
( ) ( )( )( ) ( )( )
( ) ( )( )
1
1
1
1 1 1
1 1 1
1 1 1
t t
t t
I Dt t t
I Dt t t t
t t t t
S S S
I I S I
D D I D
β χ
β χ α
α η δ
+
+
+
= minus sdot minus minus minus
= + sdot minus minus minus minus sdot
= + sdot minus minus minus sdot minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
If t = 1 and I0 = 1
1
0
1 ss
β
= minus
The proportion infected after exposure to one infected shrimpβ
Parameter estimates ndash transmission (β χ)
1 (1 (1 ) )tIt t tS S S β+ = minus sdot minus minus
Solve for β
1
1
0
0
ln(1) 1 exp
tSS
Iβ
= minus
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Parameter estimates ndash transmission (β χ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
bull 1-L jarsbull 1 shrimp per jarbull 5d incubationbull Collect mortalities (α)bull Collect survivors
Parameter estimates ndash transmission (β χ) and virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
1t t tI I I α+ = minus sdot
0
10
20
30
40
0 4 8 12 16Time (h)
Surv
ival
Parameter estimates ndash virulence (α)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
decomposition
transmission decreases by 48 per day
y-intercept = 0499
0 4 8 12Days after death
00
02
04
06
08
10
Tran
smis
sion
χ
Parameter estimates ndash decay of transmission (δ)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Parameter estimates η consumption of shrimp
24 shrimp12 shrimp
6 shrimp1 shrimp
FedFasted
decrease per hr (day) decrease per hr (day)
0 10 20 30Time (hr)
00
02
04
06
08
10
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
10
0 10 20 30Time (hr)
00
02
04
06
08
Prop
ortio
n B
iom
ass
0 10 20 300 10 20 300 10 20 300 10 20 30
17 (99)30 (100)34 (100)33 (100)
6 (79)11 (94)11 (94)12 (96)
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
Parameter estimates consumption (η) amp decomposition (δ) combined
048 + 100 - 10 048= 100
048 + 79 - 7948= 089
An infected dead shrimp retains about 0 ndash 10 of its infectivity per day
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
State Duration Transmission Product
Live Infected β
Dead Infected χ( )( )
11 1 1δ ηminus minus minus
βα
1α
( )( )1 1 1χδ ηminus minus minus
0R β χα δ η δ η
= ++ minus sdot
Life table of infection
001 06 0904 05 09 05 09
R = + =+ minus sdot
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
WSSV life cycle diagram3-host community
Susceptible
Susceptible
Susceptible Infected
Infected
Infected Dead
Dead
Dead
β31
χ31
χ11
β11λ1
λ2
λ3
micro1
micro2
micro3
β12 β21 χ21
α1 micro1
α2 micro2
α3 micro3
χ12
δ1 η1
δ2 η2
δ3 η3χ33
β33
χ13
β13
χ22
β32χ32
β22
χ23β23
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-
( ) ( )
( ) ( )( ) ( )
( ) ( )
( ) ( )( ) ( )
3
1 11
3
1 1 11
1
3
2 21
3
2 2 21
2
3
1 1 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0
0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 1
i i
i i
i i
i i
I Di i
i
I Di i
i
I Di i
i
I Di i
i
β χ
β χ α
α δ η
β χ
β χ α
α δ η
β
=
=
=
=
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus sdot minus
minus minus sdot minus minus
minus minus sdot minus
minus
prod
prod
prod
prod
( ) ( )
( ) ( )( ) ( )
1
1
1
2
2
2
3
33
331
3
3 3 31
3
1 0 0
0 0 0 0 0 0 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1
i i
i i
I Di i
i
I Di i
i
SIDSIDSIDχ
β χ α
α δ η
=
=
sdot
sdot minus
minus minus sdot minus minus minus minus sdot minus
prod
prod
WSSV 3-host community matrix model
RCN Marine Disease Modeling and Transmission Workshop ndash May 2015
- Slide Number 1
- Slide Number 2
- Slide Number 3
- Slide Number 4
- Slide Number 5
- Slide Number 6
- Slide Number 7
- Slide Number 8
- Slide Number 9
- Emergence of White spot syndrome virus
- Slide Number 11
- Slide Number 12
- Slide Number 13
- Hosts of WSSV
- WSSV Litopenaeus vannamei
- Slide Number 16
- Slide Number 17
- Slide Number 18
- Slide Number 19
- Slide Number 20
- Slide Number 21
- Slide Number 22
- Slide Number 23
- Slide Number 24
- Slide Number 25
- Slide Number 26
- Slide Number 27
- Slide Number 28
- Slide Number 29
- Slide Number 30
- Slide Number 31
- Slide Number 32
- Slide Number 33
- Slide Number 34
- Slide Number 35
- Slide Number 36
- Slide Number 37
- Slide Number 38
-