Dynamic equilibria in an epidemic model with voluntary vaccinations

Abstract

The dynamics of an epidemic model with voluntary vaccinations are studied. Individual vaccination decisions are modelled using an economic/game-theoretic approach: agents in the model decide whether to vaccinate or not by weighing the cost and benefit of vaccination and choose the action that maximizes their net benefit. It is shown that, when vaccine efficacy is low, there are parameter values for which multiple steady-state equilibria and periodic equilibria coexist. When multiplicity of steady states is obtained, which one the population reaches in some cases depends entirely on agents’ expectations concerning the future course of an epidemic and not on the initial conditions of the model. †Comments and suggestions from anonymous referees of the journal are gratefully acknowledged. This paper is dedicated to the loving memory of Lucy Hauser. © 2009 Taylor & Francis Group, LLC.