Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate

Abstract:

An SIRS epidemic model with nonlinear incidence rate is studied. It is assumed that susceptible and infectious individuals have constant immigration rates. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the analytical results.

• Periodical: Advanced Materials Research (Volumes 479-481)
• Pages: 1495-1498
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.479-481.1495
• Online since: February 2012
• Authors: Jun Hong Li, Ning Cui, Hong Kai Sun
• Keywords: Global Stability, Hopf Bifurcation, Limit Cycle, Simulation, SIRS Model

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