July 30-August 2, 2008
Society for Mathematical Biology Conference

hosted by the Centre for Mathematical Medicine, Fields Institute
held at University of Toronto, Medical Sciences Bldg


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16)Game-Theory Approaches in Epidemiology
Principal organiser: Timothy Reluga
Assistant Professor of Mathematics, Penn State University

In classical epidemiology, decisions are usually guided by a myopic perspective of ``good''. However, contemporary
challenges have made it clear that myopic planning can often lead to unintended and sometimes counterproductive results.
Government policies, for instance, that don't account for the interests of individuals may be doomed from the start.

Game theory and it's generalizations provide a means to determine optimal policies when epidemics are influenced by
many different actors with diverse perspectives. Recent research has shown how game-theory methods can be applied to
problems of vaccination, hygiene, and treatment to explain and predict various aspects of epidemic dynamics. This
minisymposia will highlight some of the exciting new research in this area.

This minisymposia will spotlight how dynamic epidemiology models can be combined with game theory models. The
presentations will show how one can extent classic models of population dynamics to incorporate individual choice,
and then show how the combination of the two can be used to ask and answer interesting scientific and practical
questions concerning the control of infectious diseases. We hope this minisymposia will promote the broad use of
the methods involved.

This minisymposia is intended for researchers with experience in mathematical epidemiology and population biology who are interested in expanding the scope of their work to incorporate aspects of choice. There will also be some natural overlap with evolutionary theory.

Speaker and Order of presentations

Frederick Chen
Chris Bauch
Euhna Shim
Sanjay Basu
Timothy Reluga

Speaker contact information:

Frederick H. Chen
Department of Economics
Wake Forest University
Box 7505
Winston-Salem, NC 27109

Chris Bauch
Department of Mathematics and Statistics
University of Guelph
50 Stone Road East
Guelph, ON N1G 2W1

Eunha Shim
Yale School of Medicine
60 College Street
P.O. Box 208034
New Haven, Connecticut 06520-8034

Sanjay Basu
Yale School of Medicine
26 High Street, #2
New Haven, CT 06510

Timothy Reluga
Departments of Mathematics and Biology
424 McAllister
Penn State University
University Park, PA 16802-6404

Talk details:

Speaker: Frederick H. Chen
Title: Voluntary Vaccinations with Rational Expectations
The dynamics of an epidemic model with voluntary vaccinations are analyzed. As is customary in economics, it is assumed that agents in the model are forward-looking and have rational expectations. That is, when they are deciding whether to vaccinate or not, they consider all the possible future consequences of their action, and, moreover, their estimates of the likelihood of future events occurring are correct. It is shown that, when vaccine efficacy is low, there are parameter values for which multiple steady state equilibria and periodic equilibria coexist. When multiplicity of steady states obtains, which one the model converges to in some cases depends entirely on agents' expectations concerning the future course of an epidemic and not on the initial conditions of the model.

Speaker: Chris Bauch
Title: Spatial localization of transmission prevents the free-rider problem in voluntary vaccination policy
Smallpox was globally eradicated several decades ago, and in many jurisdictions this occurred under a voluntary vaccination policy. However, game theory has indicated that this should not have been possible: herd immunity means that the individual incentive to vaccinate disappears once vaccine coverage is sufficiently high, if there is even a small risk associated with the vaccine. Thus, a high level of vaccine coverage under a voluntary vaccination policy is not a Nash Equilibrium. Both game theoretical and non-game theoretical analyses of this "free rider problem", or "tragedy of the commons" have usually assumed a significant degree of homogeneous mixing in infectious disease transmission. Here, we show that the free rider problem disappears once disease transmission is spatially localized. In a random network through which a generic SIR-type epidemic is spreading, and where individuals choose whether or not to vaccinate based on infection and vaccine risks, the free rider effect does not emerge until the average neighbourhood size exceeds 40-60 neighbours. Beyond this threshold, the free rider effect can result in large final epidemic sizes. Similar effects are observed with smallpox-specific parameters and natural history assumptions. This work suggests that the free rider problem may not be an issue for treatable/preventable diseases spread primarily through close contact, such as smallpox and several sexually-transmitted infections. It also suggests network models might be more appropriate for such diseases, particularly where prevalence-behaviour interactions must be incorporated.

Speaker: Eunha Shim
Title: Game theoric approach to epidemiological modeling using antiviral drug use during influenza and rubella vaccination as examples.
In general, the vaccination level determined by Nash strategy is lower than the utilitarian optimum, since unvaccinated individuals can benefit from reduced transmission in a community. However, this generalization is no longer applied to the case of rubella vaccination and antiviral drug use during pandemic influenza due to gender-dependent motivation and resistance, respectively. During pandemic influenza, individuals may experience adverse effects of
antivirals although they benefits from reduced probability and/or severity of infection. Within the community, antiviral intervention reduces transmission, but also selects for drug resistance. To evaluate how the balance among these factors results in optimal coverage for both the individual and the community, we developed an epidemiological game-theoretic model of pandemic influenza. We parameterize the model with survey data on actual perceptions regarding infection risk, the level of resistance, the efficacy and adverse effects of antivirals, and the willingness to pay for antivirals during pandemic influenza. We find that the demand for antivirals driven by self-interest during pandemic influenza would likely be far lower than that which would maximize overall utility for the population. For the case of rubella, individual decision of a male to reject vaccination indirectly harms females by increasing both the prevalence of the disease, resulting in the increased risk of CRS. Therefore, women have higher individual incentive to vaccinate against rubella than men whose symptoms are minor, if any. To determine how individual (Nash strategy) and community (utilitarian strategy) optimum levels of
accination against rubella are affected by various factors, we present an age-structured epidemiological model in the context of game theory.

Speaker: Sanjay Basu
Title: Achieving effective HPV vaccination levels in the United States: a game-theoretic modeling study
HPV vaccines provide an opportunity to reduce the incidence of cervical cancer. The optimization of public health policies to reduce cervical cancer requires anticipating the degree to which the public will adhere to vaccination recommendations.

We develop an epidemiological game theoretic model of HPV vaccination to identify potential misalignments between utilitarian vaccination
levels that are optimal for the community and those that maximize the utility for an individual. We parameterize our model with survey data
regarding actual perceptions about cervical cancer, genital warts, and vaccination against HPV, collected from parents of vaccine-eligible

Principal Findings/Significance:
We find that vaccination levels based on the perceptions of our survey respondents are much lower than vaccination levels that would maximize overall health and economic benefit to the community. We also find that addressing concerns about vaccination among parents of potential recipients may help achieve vaccination targets. However, the cost of vaccination is a more significant impediment to achieving effective vaccination levels, even in the context of the subsidization and cost-sharing schemes that are currently available.

Speaker: Timothy Reluga
Title: The effects of life history on risky behavior choice and disease transmission
Several population-game models of reasoned choice in the context of epidemics have addressed cases where individuals occupy a single life-history stage, with fixed costs for various actions. However, for many diseases, the costs and consequences of infection depend on the age of the individual at the time of infection, and individuals may vary their behaviors in response to changes in costs or future expectations. Dealing with the resulting multi-dimensional problem can present computational and conceptual challenges. This talk will present some methods for the analyses of population games with age-dependent strategies. Results including Nash and ESS properties will be established for some example epidemic models. I'll discuss the implications for planning control of endemic diseases and for population-game modelling in general.

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