Epidemic Propagation under Evolutionary Behavioral Dynamics: Stability and Bifurcation Analysis

TL;DR

This paper models epidemic spread considering individuals' protection decisions influenced by evolutionary dynamics, analyzing stability, bifurcations, and the effects of different timescales on epidemic outcomes.

Contribution

It introduces a comprehensive analysis of coupled epidemic and evolutionary dynamics, including stability, bifurcation, and timescale effects, for the first time in this context.

Findings

Existence and stability of equilibria are fully characterized.

Stability exchanges occur as parameters vary.

Timescale separation influences system behavior.

Abstract

We consider the class of SIS epidemic models in which a large population of individuals chooses whether to adopt protection or to remain unprotected as the epidemic evolves. For a susceptible individual, adopting protection reduces the probability of becoming infected but it comes with a cost that is weighed with the instantaneous risk of becoming infected. An infected individual adopting protection transmits a new infection with a smaller probability compared to an unprotected infected individual. We focus on the replicator evolutionary dynamics to model the evolution of protection decisions by susceptible and infected subpopulations. We completely characterize the existence and local stability of the equilibria of the resulting coupled epidemic and replicator dynamics. We further show how the stability of different equilibrium points gets exchanged as certain parameters change. Finally, we investigate the system behavior under timescale separation between the epidemic and the evolutionary dynamics.