Epidemiological impact of waning immunization on a vaccinated population
Mathematics, Systems Analytics Research Institute, School of Engineering and Applied Science, Aston University,
Birmingham B4 7ET, UK
a e-mail: firstname.lastname@example.org
Received in final form: 14 June 2018
Published online: 1 November 2018
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.
Key words: Statistical and Nonlinear Physics
© The Author(s) 2018. This article is published with open access at Springerlink.com
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