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A Susceptible-infected Epidemic Model with Voluntary Vaccinations

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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.

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Author information

Correspondence to Frederick H. Chen.

Additional information

I would like to thank one of the editors of the journal, Alan Hastings, for his comments and suggestions.

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Chen, F.H. A Susceptible-infected Epidemic Model with Voluntary Vaccinations. J. Math. Biol. 53, 253–272 (2006). https://doi.org/10.1007/s00285-006-0006-1

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Keywords or Phrases

  • Endemic equilibrium
  • Reproductive number
  • Dynamic programming
  • STD
  • Voluntary vaccination
  • Mass vaccination