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Cite as: J. Dehning et al., Science
10.1126/science.abb9789 (2020).
First release: 15 May 2020 www.sciencemag.org (Page numbers not final at time of first release) 1
0 .3 5 , 0 .5 1
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0 .2 0 , 0 .3 0
0 .1 2 , 0 .2 0
0 .0 6 , 0 .1 3
λ μ
D0
I
λ μ D
λ 0 .41= μ 0 .1 2= 8 .6D =0
1 9I =
0λ / μR =
03 .4R = 2 .4 4 .7
λ
0I σ
μ D
*λ λ μ= −
λ μ
λ μ
*λ
*λ 2 8%=
λ μ
λ μ
*λ 0= λ μ=
λ
0λ 0 .4 1=
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μ 0 .1 2=
0λ
1λ
1 0λ λ=
1λ 0 .41 μ=
5 0 %1 0
λ λ / 2=1
λ 0 .21 μ=
D 8 .6D =
*
1 1λ λ μ 0= −
1 0 %1 0
λ λ /1 0=1
λ 0 .04 μ=
D
*λ 0
0 1λ λ→
D
*λ λ μ= −
*λ 0
0λ
0 1λ λ→
1t
1 2λ λ→
2t
2 3λ λ→
3t
Δ )i
t
( )it
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0λ
0λ 0 .4 1= 0 .3 2 , 0 .5 1 λ
σ
0I
( )λ t0
λ 0 .43=
0 .3 5 , 0 .5 11
λ 0 .2 5=
( ) ( )*
λ λ μt t= −
0λ μ 0 .3− =
1λ μ 0 .12− =
μ 0 .1 3=
( )λ t1
λ 0 .2 5=
2λ 0 .15=
( )*
2λ λ μ 0 .0 2 0t = − =
( )λ t2
λ 0 .15=3
λ 0 .09=
( )*
3λ λ μ 0 .0 3 0t = − = − 0 .0 5, 0 .0 2− −
1 1 .4D = 3
*λ
3 0 % 1 2 % 2 %
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3 %− 5 % , 2 %− −
D
D
1 1 .4D =
( )λ t λi
λi
3 %−
D
D
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λ I
S
R μ
N
dλ
d
dλ μ
d
dμ .
d
S S I
t N
I S II
t N
RI
t
= −
= −
=
I
R S N I / 1S N
( ) ( ) ( )( )λ μ
λ μ s 0 .td I
I o lv e d b y I t I ed t
−
= − =
Δ t =
d / d Δ / ΔI t I t
n e w1
1 1
n e w
1 1
n e w n e w1
1 1
λΔ :
μΔ :
λ μ Δ .
t
t t t t
t t t t
t
t t t t t
SS S t I I
N
R R tI R
SI I tI I R
N
−
− −
− −
−
− −
− = − = −
− = =
− = − = −
tI
n e w
tI
Dn e w
tI
tC
n e w.
t t DC I
−=
0t =0
I
ˆt
C
t D
0I
λi
1, ...,i n=
it
1λ
i −λ
i
Δi
t
λ
it Δ
it λ
i
λi
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( )( )
( ) ( )
n e w1 , w ith
π 11 1 s in Φ ,
7 2
t t D
w w
C I f t
f t f t
−= −
= − − −
wf Φ
w
0θ λ , , μ , , σ , , , Φ
i i w wt D I f=
σ
( θˆ | )t
P C
θ
( ) ( ) θ θt
C C=
ˆ ˆt
C C= θ
θ
( )(θ | ) (ˆ ˆ | θ ) θ ,p C p C p ( θˆ | )p C
( )θp
( ) ( )( )ν 4( | θ ) S tu d en tT m ean θ , w id tˆ h σ θ .
t t tp C C C
= = =
t ( )θtC
ˆt
C
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( )( )μ L ogN o rm a l lo g 1 / 8 , 0 .2
μ
( )( )λ L o gN o rm a l lo g 0 .4 , 0 .5
0 .4 λ μ− 0 .2 7 5
0λ / μR =
3 .2
( )( )L o g N o rm a l lo g 8 , 0 .2D
( ) (2
H a lfC a u c h y , β 2 / π β[1 / β )x x = +
( )βO β
( )0H alfC au ch y 1 0 0I
( )1 0 0O
( )σ H alfC au chy 10
λ
5 0 %
λ
( )( )0λ L o gN o rm a l lo g 0 .4 , 0 .5
( )( )1λ L o gN o rm a l lo g 0 .2 , 0 .5
5 0 %
0λ 0 .4
( )( )2λ L ogN o rm a l lo g 1 / 8 , 0 .5
λ 5 0 %
( )( )3λ L o gN o rm a l lo g 1 / 1 6 , 0 .5
5 0 %3
λ
μ
( )1N o rm al 2 0 2 0 / 0 3 / 0 9 , 3t
( )2N o rm al 2 0 2 0 / 0 3 / 1 6 ,1t
( )3N o rm al 2 0 2 0 / 0 3 / 2 3,1t
Δi
t ( )( )Δ LogN o rm a l lo g 3 , 0 .3i
t
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( )B eta m ean 0 .7 , s td 0 .1 7w
f = =
( )Φ vonM ises m ean 0 , κ 0 .0 1w = =
( )o s
p o s t
1
lp p d = lo g ( | θ ) (θ ) θ
N
i
i
p y p d
=
o s o s
1 1, ,y y
N ( )p o s t p o s tθ (θ | , )
jp p y M=
yj
M
( )p o s tθp
2−
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λ
σ
λ λ λ
λ
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λ
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λ
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9 2 7 9 8 .3 1
8 1 9 1 6 1 3 .4 6
7 9 6 1 7 1 2 .5 3
7 8 7 1 7 1 3 .4 2
( )( )L o g N o rm al lo g 0 .4 , 0 .5
( )( )L o g N o rm al lo g 1 / 8 , 0 .2
D ( )( )L o g N o rm a l lo g 8 , 0 .2
0I ( )H alfC au ch y 1 0 0
( )H alfC au ch y 1 0
1t ( )N o rm al 2 0 2 0 / 0 3 / 0 9 , 3
2t ( )N o rm al 2 0 2 0 / 0 3 / 1 6 ,1
3t ( )N o rm al 2 0 2 0 / 0 3 / 2 3,1
Δi
t ( )( )L o g N o rm a l lo g 3 , 0 .3
0 ( )( )L o g N o rm al lo g 0 .4 , 0 .5
1 ( )( )L o g N o rm al lo g 0 .2 , 0 .5
2 ( )( )L o g N o rm al lo g 1 / 8 , 0 .5
3 ( )( )L o g N o rm a l lo g 1 / 1 6 , 0 .5
( )( )L o g N o rm al lo g 1 / 8 , 0 .2
D ( )( )L o g N o rm a l lo g 8 , 0 .2
wf ( )B eta m ean 0 .7 , s td 0 .1 7= =
Φw ( )vo n M ises m ean 0 , 0 .0 1= =
0I ( )H alfC au ch y 1 0 0
( )H alfC au ch y 1 0
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Inferring change points in the spread of COVID-19 reveals the effectiveness of interventionsJonas Dehning, Johannes Zierenberg, F. Paul Spitzner, Michael Wibral, Joao Pinheiro Neto, Michael Wilczek and Viola Priesemann
published online May 15, 2020
ARTICLE TOOLS http://science.sciencemag.org/content/early/2020/05/14/science.abb9789
MATERIALSSUPPLEMENTARY http://science.sciencemag.org/content/suppl/2020/05/14/science.abb9789.DC1
CONTENTRELATED
http://stm.sciencemag.org/content/scitransmed/9/396/eaal3653.fullhttp://stm.sciencemag.org/content/scitransmed/11/499/eaat0360.fullhttp://stm.sciencemag.org/content/scitransmed/12/534/eabb1469.fullhttp://stm.sciencemag.org/content/scitransmed/12/541/eabb5883.full
REFERENCES
http://science.sciencemag.org/content/early/2020/05/14/science.abb9789#BIBLThis article cites 36 articles, 10 of which you can access for free
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No claim to original U.S. Government WorksCopyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science.
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