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

Shutian Liu (), Yuhan Zhao () and Quanyan Zhu ()
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Shutian Liu: Tandon School of Engineering New York University
Yuhan Zhao: Tandon School of Engineering New York University
Quanyan Zhu: Tandon School of Engineering New York University

Dynamic Games and Applications, 2022, vol. 12, issue 1, No 9, 183-213

Abstract: Abstract 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 evolution 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 a structure-preserving approximation technique 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.

Keywords: Evolutionary game; Epidemic dynamics; Complex networks; Coupled dynamics; Structure-preserving approximation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13235-022-00433-3

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