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Epidemiological impact of waning immunization on a vaccinated population

  • Ewa Grela
  • Michael StichEmail author
  • Amit K Chattopadhyay
Open Access
Regular Article

Abstract

This is an epidemiological SIRV model based study that is designed to analyze the impact of vaccination in containing infection spread, in a 4-tiered population compartment comprised of susceptible, infected, recovered and vaccinated agents. While many models assume a lifelong protection through vaccination, we focus on the impact of waning immunization due to conversion of vaccinated and recovered agents back to susceptible ones. Two asymptotic states exist, the “disease-free equilibrium” and the “endemic equilibrium” and we express the transitions between these states as function of the vaccination and conversion rates and using the basic reproduction number. We find that the vaccination of newborns and adults have different consequences on controlling an epidemic. Also, a decaying disease protection within the recovered sub-population is not sufficient to trigger an epidemic at the linear level. We perform simulations for a parameter set mimicking a disease with waning immunization like pertussis. For a diffusively coupled population, a transition to the endemic state can proceed via the propagation of a traveling infection wave, described successfully within a Fisher-Kolmogorov framework.

Keywords

Statistical and Nonlinear Physics 

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Copyright information

© The Author(s) 2018

Open AccessThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Ewa Grela
    • 1
  • Michael Stich
    • 1
    Email author
  • Amit K Chattopadhyay
    • 1
  1. 1.Mathematics, Systems Analytics Research Institute, School of Engineering and Applied Science, Aston UniversityAston Triangle, BirminghamUK

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