2021/05/26 by Ioannis Kordonis, Kordonis, Ioannis, Athanasios-Rafail Lagos +3 · 1 citation
Mathematics · Medicine · Physics and Astronomy · #COVID-19 epidemiological studies #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2105.12431
openalex publication_date 2021/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Individual behaviors play an essential role in the dynamics of transmission\nof infectious diseases, including COVID--19. This paper studies a dynamic game\nmodel that describes the social distancing behaviors during an epidemic,\nassuming a continuum of players and individual infection dynamics. The\nevolution of the players' infection states follows a variant of the well-known\nSIR dynamics. We assume that the players are not sure about their infection\nstate, and thus they choose their actions based on their individually perceived\nprobabilities of being susceptible, infected or removed. The cost of each\nplayer depends both on her infection state and on the contact with others. We\nprove the existence of a Nash equilibrium and characterize Nash equilibria\nusing nonlinear complementarity problems. We then exploit some monotonicity\nproperties of the optimal policies to obtain a reduced-order characterization\nfor Nash equilibrium and reduce its computation to the solution of a\nlow-dimensional optimization problem. It turns out that, even in the symmetric\ncase, where all the players have the same parameters, players may have very\ndifferent behaviors. We finally present some numerical studies that illustrate\nthis interesting phenomenon and investigate the effects of several parameters,\nincluding the players' vulnerability, the time horizon, and the maximum allowed\nactions, on the optimal policies and the players' costs.\n