A Susceptible-infected Epidemic Model with Voluntary Vaccinations

An susceptible-infected epidemic model with endogenous behavioral changes is presented to analyze the impact of a prophylactic vaccine on disease prevalence. It is shown that, with voluntary vaccination, whether an endemic equilibrium exists or not does not depend on vaccine efficacy or the distribution of agent-types. Although an endemic equilibrium is unique in the absence of a vaccine, the availability of a vaccine can lead to multiple endemic equilibria that differ in disease prevalence and vaccine coverage. Depending on the distribution of agent-types, the introduction of a vaccine or, if one is available, a subsidy for vaccination can increase disease prevalence by inducing more risky behavior.I would like to thank one of the editors of the journal, Alan Hastings, for his comments and suggestions.