The recent COVID-19 pandemic has led to an increasing interest in the modeling and analysis of infectious diseases. The pandemic has made a significant impact on the way we behave and interact in our daily life. The past year has witnessed a strong interplay between human behaviors and epidemic spreading. In this paper, we propose an evolutionary game-theoretic framework to study the coupled evolutions of herd behaviors and epidemics. Our framework extends the classical degree-based mean-field epidemic model over complex networks by coupling it with the evolutionary game dynamics. The statistically equivalent individuals in a population choose their social activity intensities based on the fitness or the payoffs that depend on the state of the epidemics. Meanwhile, the spreading of the infectious disease over the complex network is reciprocally influenced by the players' social activities. We analyze the coupled dynamics by studying the stationary properties of the epidemic for a given herd behavior and the structural properties of the game for a given epidemic process. The decisions of the herd turn out to be strategic substitutes. We formulate an equivalent finite-player game and an equivalent network to represent the interactions among the finite populations. We develop structure-preserving approximation techniques to study time-dependent properties of the joint evolution of the behavioral and epidemic dynamics. The resemblance between the simulated coupled dynamics and the real COVID-19 statistics in the numerical experiments indicates the predictive power of our framework.
翻译:最近的COVID-19大流行导致人们对传染病的模型和分析越来越感兴趣。该流行病对我们日常生活中的行为和互动方式产生了重大影响。过去一年,人类行为和流行病蔓延之间有着强烈的相互作用。我们在本文件中提议了一个进化的游戏理论框架,以研究牧群行为和流行病同时演化的情况。我们的框架将传统的基于程度的中位流行病模式扩展至复杂的网络,将其与进化游戏动态结合起来。人口中具有统计等值的个人根据取决于流行病状况的适应性或回报选择其社会活动强度。与此同时,传染性疾病在复杂网络中的传播受到参与者社会活动的相互影响。我们通过研究该流行病的固定性特性来分析该流行病在特定流行病过程中的行为和游戏的结构性质。母体决定成为战略替代品。我们制定了一个等效的定额球员游戏和同等的网络,以代表数量有限的人口之间的相互作用。我们发展了结构-19联合预测性动态的模型和数字性动态的模型。我们发展了模型的模型和数字性动态的模型。