Abstract and Applied Analysis

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

Mingming Li and Xianning Liu

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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 F ( S , I ) and G ( I ) , 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 R 0 .

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 131257, 7 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607565

Digital Object Identifier
doi:10.1155/2014/131257

Mathematical Reviews number (MathSciNet)
MR3173270

Citation

Li, Mingming; Liu, Xianning. An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 131257, 7 pages. doi:10.1155/2014/131257. https://projecteuclid.org/euclid.aaa/1412607565


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