, Volume 63, Issue 4, pp 639-653
Date: 16 Sep 2010

Analysis of stability and bifurcation for an SEIV epidemic model with vaccination and nonlinear incidence rate

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

In this paper, an SEIV epidemic model with vaccination and nonlinear incidence rate is formulated. The analysis of the model is presented in terms of the basic reproduction number R 0. It is shown that the model has multiple equilibria and using the center manifold theory, the model exhibits the phenomenon of backward bifurcation where a stable disease-free equilibrium coexists with a stable endemic equilibrium for a certain defined range of R 0. We also discuss the global stability of the endemic equilibrium by using a generalization of the Poincaré–Bendixson criterion. Numerical simulations are presented to illustrate the results.