Original Paper

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

  • Xueyong ZhouAffiliated withSchool of Mathematical Sciences, Nanjing Normal UniversityCollege of Mathematics and Information Science, Xinyang Normal University
  • , Jingan CuiAffiliated withSchool of Science, Beijing University of Civil Engineering and Architecture Email author 

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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.

Keywords

Epidemic model Backward bifurcation Global stability Nonlinear incidence rate Bendixson criterion