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The recent COVID-19 pandemic has led to an increasing interest in themodeling and analysis of infectious diseases. The pandemic has made asignificant impact on the way we behave and interact in our daily life. Thepast year has witnessed a strong interplay between human behaviors and epidemicspreading. In this paper, we propose an evolutionary game-theoretic frameworkto study the coupled evolutions of herd behaviors and epidemics. Our frameworkextends the classical degree-based mean-field epidemic model over complexnetworks by coupling it with the evolutionary game dynamics. The statisticallyequivalent individuals in a population choose their social activity intensitiesbased 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 isreciprocally influenced by the players' social activities. We analyze thecoupled dynamics by studying the stationary properties of the epidemic for agiven herd behavior and the structural properties of the game for a givenepidemic process. The decisions of the herd turn out to be strategicsubstitutes. We formulate an equivalent finite-player game and an equivalentnetwork to represent the interactions among the finite populations. We developstructure-preserving approximation techniques to study time-dependentproperties of the joint evolution of the behavioral and epidemic dynamics. Theresemblance between the simulated coupled dynamics and the real COVID-19statistics in the numerical experiments indicates the predictive power of ourframework.

Herd Behaviors in Epidemics: A Dynamics-Coupled Evolutionary Games Approach