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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 131257, 7 pages
http://dx.doi.org/10.1155/2014/131257
Research Article

An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate

Key Laboratory of Eco-Environments in Three Gorges Reservoir Region (Ministry of Education), School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received 26 December 2013; Accepted 6 January 2014; Published 20 February 2014

Academic Editor: Weiming Wang

Copyright © 2014 Mingming Li and Xianning Liu. 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

An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions and , respectively. By constructing Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive number .