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Bistable Endemic States in a Susceptible-Infectious-Susceptible Model with Behavior-Dependent Vaccination

In: Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases

Author

Listed:
  • Alberto d’Onofrio

    (International Prevention Research Institute)

  • Piero Manfredi

    (University of Pisa, Department of Economics and Management)

Abstract

Several new vaccines have the characteristic of being “imperfect” that is their protection wanes over time and supplies only partial protection from infection. On the other hand recent research has shown that the agents’ behavioral responses have the potential to dramatically affect the dynamics and control of infections. In this paper we investigate, for a simple susceptible-infective-susceptible (SIS) infection, the dynamic interplay between human behavior, in the form of an increasing prevalence-dependent vaccine uptake function, and vaccine imperfections. The mathematical analysis of the ensuing SISV model shows a complexly articulated bifurcation structure. First, the inclusion of the simplest possible hypothesis about vaccination behavior is capable to trigger, in appropriate windows of the key parameters, phenomena of multistability of endemic states. Second, as far as the stability of the disease-free equilibrium is concerned, the model preserves the backward bifurcation which is characteristic of SIS-type infections controlled by imperfect vaccines.

Suggested Citation

  • Alberto d’Onofrio & Piero Manfredi, 2016. "Bistable Endemic States in a Susceptible-Infectious-Susceptible Model with Behavior-Dependent Vaccination," Springer Books, in: Gerardo Chowell & James M. Hyman (ed.), Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases, pages 341-354, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-40413-4_21
    DOI: 10.1007/978-3-319-40413-4_21
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