Emergent and re-emergent challenges in
the theory of infectious diseases
South Africa
June, 2007
www.noveltp.com
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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
image.guardian.co.uk/
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• They also are complex adaptive systems,
integrating phenomena at multiple scales
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www.who.int
www.nobel.org
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Integrating these multiple scales is
one major challenge
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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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http://edie.cprost.sfu.ca/gcnet
Significant management puzzles
remain
• Whom should we vaccinate?
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www.calcsea.org
Whom should we vaccinate?
• Those at greatest risk?
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www.nursingworld.org
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Whom should we vaccinate?
• Or those who pose greatest risk to others?
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www-personal.umich.edu/~mejn
Other management puzzles:
Problems 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
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)
Susceptible
S
Infectious
I
Removed
R
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Simplest model
dI /dt  SI  I  I
deaths
recovered
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For spread:
S
Rs 
1
 
Condition for spread in a naïve population
1
R 0  N 
1

Secondary Average
infections/ infectious
time
period
Thus R0 is the #secondary/primary infection.
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Interpretation if threshold is exceeded
1. With no new recruits, outbreak and collapse
2. With new births, get stable equilibrium
3. Oscillations require a more complicated model
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Complications
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• New immigrants
H.M.S. Bounty
www.lareau.org
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Complications
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• New immigrants
• Demography
www.lareau.org
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Complications
• New immigrants
• Demography
• Heterogeneous mixing patterns
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Complications
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New immigrants
Demography
Heterogeneous mixing patterns
Genetic changes in host
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Complications
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New immigrants
Demography
Heterogeneous mixing patterns
Genetic changes in host
Multiple strains/diseases
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Complications
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New immigrants
Demography
Heterogeneous mixing patterns
Genetic changes in host
Multiple strains/diseases
Vectors
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Complications
•
•
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•
•
New immigrants
Demography
Heterogeneous mixing patterns
Genetic changes in host
Multiple strains/diseases
Vectors
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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
R2
Recovered 1,2
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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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Summary:
Understanding 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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www.aisobservers.com
Problems of The Commons
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Fisheries
Aquifers
Pollution
Vaccines
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images.usatoday.com
Problems of The Commons
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Fisheries
Aquifers
Pollution
Vaccines
Antibiotics
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www.bath.ac.uk
Antibiotic resistance is on the rise
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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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Huang et al, Emerging Infectious Diseases, 2002
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. 55
(San Francisco County)
Antibiotic resistance spreads to novel bacteria
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www.mja.com.au
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
admission…carriers
• 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 movement
Basic model structure
k
i indicates group, such as elderly
j,k indicate subpopulations, such as hospital, community
q indicates proportion (fixed)
Model assumes admit=discharge
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Smith et al, PNAS 2004
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
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