Interplay of Strategic Decision Making and Spread of Epidemics

Abstract

Infectious diseases or epidemics spread through human society via social interactions among infected and healthy individuals. In this talk, we explore the coupled evolution of the epidemic and protection adoption behavior of humans.

In the first part of the talk, we focus on the class of susceptible-infected-susceptible (SIS) epidemic model where individuals choose whether to adopt protection or not based on the trade-off between the cost of adopting protection and the risk of infection; the latter depends on the current prevalence of the epidemic and the fraction of individuals who adopt protection in the entire population. We define the coupled epidemic-behavioral dynamics by modeling the evolution of individual protection adoption behavior according to the replicator dynamics. We fully characterize the equilibria and their stability properties. We further analyze the coupled dynamics under timescale separation when individual behavior evolves faster than the epidemic, and characterize the equilibria of the resulting discontinuous hybrid dynamical system. Numerical results illustrate how the coupled dynamics exhibits oscillatory behavior and convergence to sliding mode solutions under suitable parameter regimes.

In the second part of the talk, we discuss a dynamic population game model to capture individual behavior against susceptible-asymptomatic-infected-recovered (SAIR) epidemic model. Each node chooses whether to activate (i.e., interact with others), how many other individuals to interact with, and which zone to move to in a time-scale which is comparable with the epidemic evolution. We define and analyze the notion of equilibrium in this game, and investigate the transient behavior of the epidemic spread in a range of numerical case studies, providing insights on the effects of the agents' degree of future awareness, strategic migration decisions, as well as different levels of lockdown and other interventions.