Emergent and reemergent challenges in

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• Emergent and re-emergent challenges in
• the theory of infectious diseases

South Africa June, 2007
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The theory of infectious diseases has a rich
history
Sir Ronald Ross 1857-1932
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But prediction is difficult

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

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

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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
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Significant management puzzles remain

• Whom should we vaccinate?

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Whom should we vaccinate?

• Those at greatest risk?

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Whom should we vaccinate?

• Or those who pose greatest risk to others?

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Other management puzzlesProblems of the Commons

• Individual benefits/costs vs. group
  benefits/costs
• Vaccination
• Antibiotic use
• Hospitals and nursing homes vs. health-care
  providers vs. individuals
• These 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 fluctuations
• Antibiotic resistance and other problems of the
  Commons

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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
fluctuations
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Influenza 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 strains
• Gradual replacement at level of subtypes
• Recurrence at level of clusters

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Standard SIR Model (No latency)
SusceptibleS
RemovedR
Infectious I
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Simplest model
recovered
deaths
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For spread
Condition for spread in a naïve population
Thus R0 is the secondary/primary infection.
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Interpretation if threshold is exceeded

• 1. With no new recruits, outbreak and collapse
• With new births, get stable equilibrium
• Oscillations require a more complicated model

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Complications

• New immigrants

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H.M.S. Bounty
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Complications

• New immigrants
• Demography

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Complications

• New immigrants
• Demography
• Heterogeneous mixing patterns

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Complications

• New immigrants
• Demography
• Heterogeneous mixing patterns
• Genetic changes in host

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Complications

• New immigrants
• Demography
• Heterogeneous mixing patterns
• Genetic changes in host
• Multiple strains/diseases

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Complications

• New immigrants
• Demography
• Heterogeneous mixing patterns
• Genetic changes in host
• Multiple strains/diseases
• Vectors

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Complications

• New immigrants
• Demography
• Heterogeneous mixing patterns
• Genetic changes in host
• Multiple strains/diseases
• Vectors

www.lareau.org
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Oscillations

• Stochastic factors
• Seasonal forcing (e.g., in transmission rates)
• Long periods of temporary immunity
• Other explicit delays (e.g., incubation periods)
• Age structure
• Non-constant population size
• Non-bilinear transmission coefficients
• Interactions with other diseases/strains

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Oscillations

• Stochastic factors
• Seasonal forcing (e.g., in transmission rates)
• Long periods of temporary immunity
• Other explicit delays (e.g., incubation periods)
• Age structure
• Non-constant population size
• Non-(bilinear) transmission coefficients
• Interactions with other diseases/strains

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Oscillations

• Stochastic factors
• Seasonal forcing (e.g., in transmission rates)
• Long periods of temporary immunity
• Other explicit delays (e.g., incubation periods)
• Age structure
• Non-constant population size
• Non-(bilinear) transmission coefficients
• Interactions with other diseases/strains

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Oscillations

• Stochastic factors
• Seasonal forcing (e.g., in transmission rates)
• Long periods of temporary immunity
• Other explicit delays (e.g., incubation periods)
• Age structure
• Non-constant population size
• Non-(bilinear) transmission coefficients
• Interactions with other diseases/strains

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Oscillations

• Seasonal forcing (e.g., in transmission rates)
• Can interact with endogenous oscillations to
  produce chaos
• Age structure
• Creates implicit delays
• Interactions with other diseases/strains
• Includes, therefore, genetic change in pathogen

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Interacting strains or diseases
Susceptible
Infectious 1
Recovered 1
Infectious 2
Infectious 2
R1
Recovered 2
Infectious 1
Recovered 1,2
R2
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Understanding endogenous oscillations

• Age-structured models can produce damped
  oscillations (Schenzele, Castillo-Chavez et al.)
• Two-strain models can produce damped oscillations
  (Castillo-Chavez et al.)
• Coupling these may lead to sustained periodic or
  other oscillations

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SummaryUnderstanding endogenous oscillations

• Age-structure
• Epidemiology
• Genetics
• all have characteristic scales of oscillation
  that can interact with each other, and with
  seasonal forcing

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Lecture outline

• Periodicities and fluctuations
• Antibiotic resistance and other problems of the
  Commons

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Problems of The Commons

• Fisheries
• Aquifers
• Pollution

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Problems of The Commons

• Fisheries
• Aquifers
• Pollution
• Vaccines

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Problems of The Commons

• Fisheries
• Aquifers
• Pollution
• Vaccines
• Antibiotics

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 antibiotics
  have given us against a wide spectrum of diseases

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Reasons for rise of antibiotic resistance

• Agricultural uses
• Overuse by physicians
• Hospital spread (nosocomial infections)

www.history.navy.mil/ac
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Hospitals are a major source of spread
Huang et al, Emerging Infectious Diseases, 2002
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)
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Antibiotic resistance spreads to novel bacteria
www.mja.com.au
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Antibiotic use

• Hospitals and communities create a metapopulation
  framework (Lipsitch et al Smith et al)
• Spatially- explicit strategies could help
• Economics dominates control

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Individuals may harbor ARB on admissioncarriers

• How do increases in the general population
  contribute to infections by ARB in the hospital,
  and what can be done about it?
• Develop metapopulation models exploring
  colonization of hosts by antibiotic resistant
  strains

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Individual movementBasic model structure
k
i indicates group, such as elderly j,k indicate
subpopulations, such as hospital, community q
indicates proportion (fixed) Model assumes
admitdischarge
Smith et al, PNAS 2004
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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 hospitals
• Compute optimal investment for a single hospital
  in controlling antibiotic resistance
• Compute game-theoretic optimal strategy in a
  mixed population, with discounting
• Investment decreases with city size

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Conclusions

• Infectious diseases have a rich modeling history
• Great challenges for behavioral sciences
• Relevant methods will span a broad range