Spatial Population Games in Epidemiology and Ecology

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).In this project, the investigators are using mathematical methods from game theory, dynamical systems, and stochastic processes to study how behavioral patterns emerge in spatially structured populations, to help account for these patterns in the development of natural-resource, health, and environmental management programs. New advances in the applications of game-theoretic methods to epidemiology problems show how large-population approximations can be used to predict the limitations of specific public health measures. By leveraging the substantial body of existing research on the dynamics of populations distributed in space, including metapopulations and reaction-diffusion equations, this project applies and extends the recent research to explain patterns the daily activities of individuals. In particular, the investigators are addressing epidemiological questions of how geographically heterogeneous risks of infection influence prophylactic measures. The team seeks to understand how spatially explicit mixing alters Nash equilibrium strategies and determines how far the influence from hot spots of risk can extend. We are also undertaking studies to expand classical theories like that of Isaacs so that we can study basic behaviors in few-player games like predation avoidance which are potentially important in the dynamics of ecosystems. These explorations should reveal foundational challenges regarding the specification of problems and their solution, and translational challenges like algorithm development and numerical approximation. The project as a whole opens up new exciting avenues of applied mathematics research in spatial ecology and sustainable management that intersects the fields of ecology, economics, sociology, and epidemiology, which can attract talented junior and senior mathematicians in analysis, dynamics, and numerics. The graduate student training funded by the grant is highly valued in both industry and government.The theory of the sustainable management of resources, ecosystems, communities, and our environment is complex, requiring the simultaneous accounting of economic processes, natural processes, and the feedbacks between the two. One aspect of sustainable management theory needing more attention is the identification of how geography and spatial distributions of resources and risks mediate the feedbacks between economic and natural processes; from pollution to water supplies to agriculture, the actions of economic agents can have unintended consequences for near-by and distant neighbors. Geographic effects can make it hard to anticipate the full consequences of an economic activity or regulatory action, to the extent that important information is often missing in the policy-design process. Mathematical models like the ones under development are valuable supplements to this missing information, and help us allocate scarce community and government resources efficiently. This project contributes to the development of some basic predictions of how populations should react to the geographically dispersed risks, allowing more rational risk mitigation. These results and the research they stimulate lead to a better understand ecological processes so that the nation may confront the long-term environmental challenges that now exist.