, Volume 63, Issue 4, pp 639-653

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

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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.

This work is supported by the National Natural Science Foundation of China (Nos. 10771104 and 11071011), Program for Innovative Research Team (in Science and Technology) in University of Henan Province and Innovation Scientists and Technicians Troop Construction Projects of Henan Province, Program for Key Laboratory of Simulation and Control for Population Ecology in Xinyang Normal University (No. 201004), Natural Science Foundation of the Education Department of Henan Province (No. 2009B110020) and Colleges and Universities in Jiangsu Province Plans to Graduate Research.