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Volume 4, Number 4, 2014, Pages 405-418                                                                DOI:10.11948/2014023
Stability Analysis of an SEIS Epidemic Model with Nonlinear Incidence and Time Delay
Xiaohong Tian,Rui Xu
Keywords:SEIS epidemic model
Abstract:
      In this paper, an SEIS epidemic model with nonlinear incidence and time delay is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the model is established. By using suitable Lyapunov functional and LaSalle's invariance principle, it is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. If the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global stability of the endemic equilibrium. Numerical simulations are carried out to illustrate the theoretical results.
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