1 emergent and re-emergent challenges in the theory of infectious diseases south africa june, 2007

1 Emergent and re-emergent challenges in

the theory of infectious diseases

www.noveltp.com

South AfricaJune, 2007

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The theory of infectious diseases has a rich history

Sir Ronald RossSir Ronald Ross 1857-19321857-1932

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But prediction is difficultBut prediction is difficult

• Disease systems are complex, characterized by nonlinearities and sudden flips

image.guardian.co.uk/

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• They also are complex adaptive systemscomplex adaptive systems, integrating phenomena at multiple scales

encarta.msn.com

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are needed to see this picture.

www.who.intwww.nobel.org

lshtm.ac.uk



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Integrating these multiple scales is one major challenge

• Pathogen

• Host individual

• Host population dynamics

• Pathogen genetics

• Host genetics

• Vector

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Despite a century of elegant theory, new diseases emerge, old reemerge

http://edie.cprost.sfu.ca/gcnet

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Significant management puzzles remain

• Whom should we vaccinate?Whom should we vaccinate?



www.calcsea.org

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Whom should we vaccinate?

• Those at greatest risk?Those at greatest risk?



www.nursingworld.org



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Whom should we vaccinate?

• Or those who pose greatest risk to others?Or those who pose greatest risk to others?

www-personal.umich.edu/~mejn



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Other management puzzles:Problems of the Commons

• Individual benefits/costs vs. group benefits/costsIndividual benefits/costs vs. group benefits/costs– VaccinationVaccination– Antibiotic useAntibiotic use

• Hospitals and nursing homes vs. health-care Hospitals and nursing homes vs. health-care providers vs. individualsproviders vs. individuals

These introduce game-theoretic problemsThese introduce game-theoretic problems

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Antibiotic resistance threatens the effectiveness of our most potent

weapons against bacterial infections



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Lecture outline

• Periodicities and fluctuationsPeriodicities and fluctuations

• Antibiotic resistance and other problems of the Antibiotic resistance and other problems of the CommonsCommons

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Many important diseases exhibit oscillations on multiple temporal and

spatial scales

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Measles in the U.K.; Grenfell et al. 2001 (Nature)

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Control must deal with temporal and spatial fluctuationsControl must deal with temporal and spatial fluctuations

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Influenza global spreadInfluenza global spread

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Influenza A reemerges year after year, despite the fact that infection leads to

lifetime immunity to a strain

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U.S. mortality in the 20th century

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The “Spanish Flu” of 1918

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Bush, Fitch, Cox

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Timeseries of viral clusters

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Fluctuations in influenza A

• Rapid replacement at level of individual strainsRapid replacement at level of individual strains

• Gradual replacement at level of subtypesGradual replacement at level of subtypes

• Recurrence at level of clustersRecurrence at level of clusters

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Standard SIR Model(No latency)

SusceptibleS RemovedR

Infectious I

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Simplest model

dI /dt SI I Ideaths recovered

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R0 N 1

1

Secondaryinfections/

time

Average infectious

period

Thus R0 is the #secondary/primary infection.

Condition for spread in a naïve populationCondition for spread in a naïve population

Rs S

1For spread: For spread:

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Interpretation if threshold is exceeded

1. 1. With no new recruits, outbreak and collapseWith no new recruits, outbreak and collapse

2.2. With new births, get stable equilibriumWith new births, get stable equilibrium

3.3. Oscillations require a more complicated modelOscillations require a more complicated model

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Complications

• New immigrantsNew immigrants



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H.M.S. BountyH.M.S. Bounty

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Complications


• DemographyDemography



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Complications



• Heterogeneous mixing patternsHeterogeneous mixing patterns



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Complications




• Genetic changes in hostGenetic changes in host



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Complications





• Multiple strains/diseasesMultiple strains/diseases



www.lareau.org

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Complications






• VectorsVectors



www.lareau.org

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Complications






• VectorsVectors



www.lareau.org

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Oscillations

• Stochastic factorsStochastic factors

• Seasonal forcing (e.g., in transmission rates)Seasonal forcing (e.g., in transmission rates)

• Long periods of temporary immunityLong periods of temporary immunity

• Other explicit delays (e.g., incubation periods)Other explicit delays (e.g., incubation periods)

• Age structureAge structure

• Non-constant population sizeNon-constant population size

• Non-bilinear transmission coefficientsNon-bilinear transmission coefficients

• Interactions with other diseases/strainsInteractions with other diseases/strains

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Oscillations







• Non-(bilinear) transmission coefficientsNon-(bilinear) transmission coefficients


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Oscillations









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Oscillations









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Oscillations


– Can interact with endogenous oscillations to produce Can interact with endogenous oscillations to produce chaoschaos


– Creates implicit delaysCreates implicit delays


– Includes, therefore, genetic change in pathogenIncludes, therefore, genetic change in pathogen

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Susceptible

Infectious 2

Recovered 2

Infectious 1

Infectious 1 Recovered 1,2

Recovered 1

Infectious 2

Interacting strains or diseasesInteracting strains or diseases

R2

R1

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Understanding endogenous oscillations

• Age-structured models can produce damped Age-structured models can produce damped oscillations (Schenzele, Castillo-Chavez et al.)oscillations (Schenzele, Castillo-Chavez et al.)

• Two-strain models can produce damped Two-strain models can produce damped oscillations (Castillo-Chavez et al.) oscillations (Castillo-Chavez et al.)

• Coupling these may lead to sustained periodic or Coupling these may lead to sustained periodic or other oscillationsother oscillations

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Summary:Understanding endogenous oscillations

• Age-structure Age-structure

• Epidemiology Epidemiology

• GeneticsGenetics

all have characteristic scales of oscillation that can all have characteristic scales of oscillation that can interact with each other, and with seasonal forcing interact with each other, and with seasonal forcing

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Lecture outline

• Periodicities and fluctuationsPeriodicities and fluctuations

• Antibiotic resistance and other problems of the Antibiotic resistance and other problems of the CommonsCommons

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Problems of The Commons

• FisheriesFisheries

• AquifersAquifers

• PollutionPollutionQuickTime™ and a

TIFF (Uncompressed) decompressorare needed to see this picture.

www.aisobservers.com

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• PollutionPollution

• VaccinesVaccines

pubs.acs.org



images.usatoday.com

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• PollutionPollution

• VaccinesVaccines

• AntibioticsAntibiotics

www.bath.ac.uk

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Antibiotic resistance is on the rise

www.wellcome.ac.uk

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Would you deny your child antibiotics to maintain global effectiveness?

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Antibiotic resistance is an increasing problem

We are rapidly losing the benefits We are rapidly losing the benefits antibiotics have given us against a wide antibiotics have given us against a wide

spectrum of diseasesspectrum of diseases

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Reasons for rise of antibiotic resistance

• Agricultural usesAgricultural uses

• Overuse by physiciansOveruse by physicians

• Hospital spread (nosocomial infections)Hospital spread (nosocomial infections)

www.history.navy.mil/ac

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Hospitals are a major source of spread

Methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant Enterococcus (VRE) isolates by hospital day of admission. Early peak corresponds to patients entering the hospital with MRSA or VRE bacteremia. Later peak likely represents nosocomial acquisition. (San Francisco County)

Huang et al, Emerging Infectious Diseases, 2002

56www.mja.com.au

Antibiotic resistance spreads to novel bacteriaAntibiotic resistance spreads to novel bacteria

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Antibiotic useAntibiotic use

• Hospitals and communities create a metapopulation framework (Lipsitch et al; Smith Smith et al)

• Spatially- explicit strategies could help

• Economics dominates control

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Individuals may harbor ARB on admission…carriers

• How do increases in the general population contribute How do increases in the general population contribute to infections by ARB in the hospital, and what can be to infections by ARB in the hospital, and what can be done about it?done about it?

• Develop metapopulation models exploring colonization Develop metapopulation models exploring colonization of hosts by antibiotic resistant strainsof hosts by antibiotic resistant strains

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Individual movementBasic model structure

Smith et al, PNAS 2004

i indicates group, such as elderlyi indicates group, such as elderlyj,k indicate subpopulations, such as hospital, communityj,k indicate subpopulations, such as hospital, communityq indicates proportion (fixed)q indicates proportion (fixed)Model assumes admit=dischargeModel assumes admit=discharge

kk

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Bigger hospitals have bigger problems

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Hospitals in larger cities have larger problems

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Smith, Levin, Laxminarayan

• Consider a game among hospitalsConsider a game among hospitals

• Compute optimal investment for a single hospital Compute optimal investment for a single hospital in controlling antibiotic resistancein controlling antibiotic resistance

• Compute game-theoretic optimal strategy in a Compute game-theoretic optimal strategy in a mixed population, with discountingmixed population, with discounting

• Investment decreases with city sizeInvestment decreases with city size

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Conclusions

• Infectious diseases have a rich modeling historyInfectious diseases have a rich modeling history

• Great challenges for behavioral sciencesGreat challenges for behavioral sciences

• Relevant methods will span a broad range Relevant methods will span a broad range

1 emergent and re-emergent challenges in the theory of infectious diseases south africa june, 2007

Documents

cagcnet slide

cox slide

strain slide

nature slide

mejn slide

complicated model slide

th century slide

influenza global spread