Nonlinear Dynamics

, Volume 63, Issue 4, pp 639–653

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

Original Paper

DOI: 10.1007/s11071-010-9826-z

Cite this article as:
Zhou, X. & Cui, J. Nonlinear Dyn (2011) 63: 639. doi:10.1007/s11071-010-9826-z


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 disease-free equilibrium coexists with a stable endemic equilibrium for a certain defined range of R0. 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.


Epidemic modelBackward bifurcationGlobal stabilityNonlinear incidence rateBendixson criterion

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.School of Mathematical SciencesNanjing Normal UniversityNanjingP.R. China
  2. 2.College of Mathematics and Information ScienceXinyang Normal UniversityXinyangP.R. China
  3. 3.School of ScienceBeijing University of Civil Engineering and ArchitectureBeijingP.R. China