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16 Sep 2010
Analysis of stability and bifurcation for an SEIV epidemic model with vaccination and nonlinear incidence rate
 Xueyong Zhou,
 Jingan Cui
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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 diseasefree 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.
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 Title
 Analysis of stability and bifurcation for an SEIV epidemic model with vaccination and nonlinear incidence rate
 Journal

Nonlinear Dynamics
Volume 63, Issue 4 , pp 639653
 Cover Date
 20110301
 DOI
 10.1007/s110710109826z
 Print ISSN
 0924090X
 Online ISSN
 1573269X
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Epidemic model
 Backward bifurcation
 Global stability
 Nonlinear incidence rate
 Bendixson criterion
 Industry Sectors
 Authors

 Xueyong Zhou ^{(1)} ^{(2)}
 Jingan Cui ^{(3)}
 Author Affiliations

 1. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210046, Jiangsu, P.R. China
 2. College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000, Henan, P.R. China
 3. School of Science, Beijing University of Civil Engineering and Architecture, Beijing, 100044, P.R. China