An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate. (20th February 2014)

• Record Type: Journal Article
• Authors: Li, Mingming; Liu, Xianning
• Other Names: Wang Weiming Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-02-20
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/131257
• Languages: English
• ISSNs: 1085-3375

Abstract

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 .