Spatial Population Games in Epidemiology and Ecology

流行病学和生态学中的空间人口博弈

• 批准号: 0920822
• 负责人: Timothy Reluga
• 金额: $ 18万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0920822&HistoricalAwards=false
• 关键词: Spatial; Population; Games; Epidemiology; Ecology

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.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。在这个项目中，研究人员使用博弈论，动力系统和随机过程的数学方法来研究行为模式如何出现在空间结构化的人群中，以帮助解释这些模式在自然资源，健康和环境管理计划的发展。 博弈论方法在流行病学问题中应用的新进展表明，大人口近似可以用来预测特定公共卫生措施的局限性。 通过利用大量关于空间分布种群动态的现有研究，包括集合种群和反应扩散方程，该项目应用并扩展了最近的研究，以解释个人日常活动的模式。 特别是，研究人员正在解决流行病学问题，即地理上不同的感染风险如何影响预防措施。 该团队试图了解空间显式混合如何改变纳什均衡策略，并确定风险热点的影响可以延伸多远。 我们还在进行研究，以扩展像艾萨克斯这样的经典理论，这样我们就可以研究在生态系统动态中潜在重要的捕食回避等少数玩家游戏中的基本行为。 这些探索应该揭示关于问题的规范及其解决方案的基本挑战，以及算法开发和数值逼近等转化挑战。 该项目作为一个整体开辟了新的令人兴奋的途径，应用数学研究在空间生态学和可持续管理，交叉领域的生态学，经济学，社会学和流行病学，这可以吸引有才华的初级和高级数学家在分析，动力学和数值。 研究生的培养受到了产业界和政府的高度重视。资源、生态系统、社区和环境的可持续管理理论非常复杂，需要同时考虑经济过程、自然过程以及两者之间的反馈。 可持续管理理论需要更多关注的一个方面是确定资源和风险的地理和空间分布如何调节经济和自然过程之间的反馈;从污染到供水到农业，经济主体的行为可能会对附近和遥远的邻居产生意想不到的后果。 由于地理影响，很难预测一项经济活动或管制行动的全部后果，以至于在政策设计过程中往往缺少重要的信息。 正在开发的数学模型是对这些缺失信息的宝贵补充，有助于我们有效地分配稀缺的社区和政府资源。 该项目有助于制定一些基本预测，以预测人口应如何应对地理分散的风险，从而实现更合理的风险缓解。 这些结果和它们所激发的研究导致更好地理解生态过程，使国家可以面对目前存在的长期环境挑战。