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A Reality of Its Own Read chapter Read first chapter

2016 | OriginalPaper | Chapter

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

Authors : Alberto d’Onofrio, Piero Manfredi

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

Publisher: Springer International Publishing

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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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previous chapter Capturing Household Transmission in Compartmental Models of Infectious Disease
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Metadata
Title
Bistable Endemic States in a Susceptible-Infectious-Susceptible Model with Behavior-Dependent Vaccination
Authors
Alberto d’Onofrio
Piero Manfredi
Copyright Year
2016
Book
Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases

Print ISBN: 978-3-319-40411-0

Electronic ISBN: 978-3-319-40413-4

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-40413-4_21