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International Journal of Differential Equations
Volume 2012 (2012), Article ID 408637, 13 pages
http://dx.doi.org/10.1155/2012/408637
Research Article

Qualitative Analysis of Delayed SIR Epidemic Model with a Saturated Incidence Rate

Department of Mathematical Sciences, College of Science, UAE University, 17551 Al-Ain, UAE

Received 23 October 2012; Accepted 6 December 2012

Academic Editor: Ephraim Agyingi

Copyright © 2012 Fathalla A. Rihan and M-. Naim Anwar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a delayed SIR epidemic model in which the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the susceptible. We investigate the qualitative behaviour of the model and find the conditions that guarantee the asymptotic stability of corresponding steady states. We present the conditions in the time lag in which the DDE model is stable. Hopf bifurcation analysis is also addressed. Numerical simulations are provided in order to illustrate the theoretical results and gain further insight into the behaviour of this system.