Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes. (21st July 2014)

• Record Type: Journal Article
• Authors: Wang, Ying; Teng, Zhidong; Rehim, Mehbuba
• Other Names: Guerrini Luca Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2014(2014)
• Publication Date: 2014-07-21
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2014/472746
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We investigate the dynamical behaviors of a class of discrete SIRS epidemic models with nonlinear incidence rate and varying population sizes. The model is required to possess different death rates for the susceptible, infectious, recovered, and constant recruitment into the susceptible class, infectious class, and recovered class, respectively. By using the inductive method, the positivity and boundedness of all solutions are obtained. Furthermore, by constructing new discrete type Lyapunov functions, the sufficient and necessary conditions on the global asymptotic stability of the disease-free equilibrium and endemic equilibrium are established.