Epidemic Population Games With Nonnegligible Disease Death Rate

A recent article that combines normalized epidemic compartmental models and population games put forth a system theoretic approach to capture the coupling between a population's strategic behavior and the course of an epidemic. It introduced a payoff mechanism that governs the population's strategic choices via incentives, leading to the lowest endemic proportion of infectious individuals subject to cost constraints. Under the assumption that the disease death rate is approximately zero, it uses a Lyapunov function to prove convergence and formulate a quasi-convex program to compute an upper bound for the peak size of the population's infectious fraction. In this article, we generalize these results to the case in which the disease death rate is nonnegligible. This generalization brings on additional coupling terms in the normalized compartmental model, leading to a more intricate Lyapunov function and payoff mechanism. Moreover, the associated upper bound can no longer be determined exactly, but it can be computed with arbitrary accuracy by solving a set of convex programs.