Hopf bifurcation in two SIRS density dependent epidemic models

28Citations
Citations of this article
22Readers
Mendeley users who have this article in their library.

This article is free to access.

Abstract

This paper uses two SIRS type epidemiological models to examine the impact on the spread of disease caused by vaccination when the immunity gained from such an intervention is not lifelong. This occurs, for example, in vaccination against influenza. We assume that susceptible individuals become immune immediately after vaccination and that immune individuals become susceptible to infection after a sufficient lapse of time. In our first model, we consider a constant contact rate between infectious and susceptible individuals, whereas in our second model this depends on the current size of the population. The death rate in both models depends on population density. We examine the different types of dynamic and long term behaviour possible in our models and in particular examine the existence and stability of equilibrium solutions. We find that Hopf bifurcation is theoretically possible but appears not to occur for realistic parameter values. Numerical simulations confirm the analytical results. The paper concludes with a brief discussion. © 2004 Elsevier Ltd. All rights reserved.

Cite

CITATION STYLE

APA

Greenhalgh, D., Khan, Q. J. A., & Lewis, F. I. (2004). Hopf bifurcation in two SIRS density dependent epidemic models. Mathematical and Computer Modelling, 39(11–12), 1261–1283. https://doi.org/10.1016/j.mcm.2004.06.007

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free