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

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

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.

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Acknowledgments

The authors want to thank the anonymous referees for their important suggestions (e.g. the remark in Sect. 4), and the editors of this book, G. Chowell-Puente and J. (Mac) Hyman, for their kind assistance and remarkable patience....

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Authors and Affiliations

  1. International Prevention Research Institute, 95 Cours Lafayette, 69006, Lyon, France

    Alberto d’Onofrio

  2. Department of Economics and Management, University of Pisa, Via Ridolfi 10, 56124, Pisa, Italy

    Piero Manfredi

Authors
  1. Alberto d’Onofrio
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  2. Piero Manfredi
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Corresponding author

Correspondence to Alberto d’Onofrio .

Editor information

Editors and Affiliations

  1. School of Public Health, Georgia State University, Atlanta, Georgia, USA

    Gerardo Chowell

  2. Department of Mathematics, Tulane University, New Orleans, Louisiana, USA

    James M. Hyman

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d’Onofrio, A., Manfredi, P. (2016). Bistable Endemic States in a Susceptible-Infectious-Susceptible Model with Behavior-Dependent Vaccination. In: Chowell, G., Hyman, J. (eds) Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases. Springer, Cham. https://doi.org/10.1007/978-3-319-40413-4_21

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