TITLE:
Analysis of a Delayed SIR Model with Exponential Birth and Saturated Incidence Rate
AUTHORS:
Wanwan Wang, Maoxing Liu, Jinqing Zhao
KEYWORDS:
Exponential Birth; SIR Model; Time Delay; Hurwitz Criterion; Hopf Bifurcation
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.10B,
October
4,
2013
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 appropriatecritical value. At last, some
numerical simulations of the model are given to illustrate the main theoretical
results.