Analysis of a Delayed SIR Model with Exponential Birth and Saturated Incidence Rate

Wanwan Wang, Maoxing Liu, Jinqing Zhao

Department of Mathematics, North University of China, Taiyuan, China.

DOI: 10.4236/am.2013.410A2006                

Abstract

In this paper, a delayed SIR model with exponential demographic structure and the saturated incidence rate is formulated. The stability of the equilibria is analyzed with delay: the endemic equilibrium is locally stable without delay; and the endemic equilibrium is stable if the delay is under some condition. Moreover the dynamical behaviors from stability to instability will change with an appropriate critical value. At last, some numerical simulations of the model are given to illustrate the main theoretical results.

Keywords

Exponential Birth; SIR Model; Time Delay; Hurwitz Criterion; Hopf Bifurcation

Conflicts of Interest

The authors declare no conflicts of interest.

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