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A susceptible-infected epidemic model with voluntary vaccinations. (English) Zbl 1098.92044
Summary: A 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.
MSC:
92C60Medical epidemiology
90C39Dynamic programming
92D30Epidemiology
90C90Applications of mathematical programming
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