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

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 R0. 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 diseasefree equilibrium coexists with a stable endemic equilibrium for a certain defined range of R0. We also disThis 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. X. Zhou School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, Jiangsu, P.R. China X. Zhou College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, Henan, P.R. China e-mail: [email protected] J. Cui ( ) School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, P.R. China e-mail: [email protected] cuss the global stability of the endemic equilibrium by using a generalization of the Poincaré–Bendixson criterion. Numerical simulations are presented to illustrate the results.