Coupled Evolutionary Behavioral and Disease Dynamics under Reinfection Risk

TL;DR

This paper investigates how individual protection decisions influence epidemic spread in SIS and SIRI models, revealing oscillatory behaviors and stability properties through coupled behavioral and disease dynamics analysis.

Contribution

It introduces a game-theoretic framework for coupled epidemic-behavioral dynamics, fully characterizes equilibria, and analyzes hybrid systems under different timescale assumptions.

Findings

Coupled dynamics can lead to oscillations in infection levels.

Equilibria stability depends on model parameters.

Behavioral adaptation influences epidemic outcomes.

Abstract

We study the interplay between epidemic dynamics and human decision making for epidemics that involve reinfection risk; in particular, the susceptible-infected-susceptible (SIS) and the susceptible-infected-recovered-infected (SIRI) epidemic models. In the proposed game-theoretic setting, 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. For the SIS epidemic, 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 for both SIS and SIRI models. Numerical results illustrate how the coupled dynamics exhibits oscillatory behavior and convergence to sliding mode solutions under suitable parameter regimes.