Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment. (21st November 2013)

• Record Type: Journal Article
• Authors: Li, Junhong; Cui, Ning
• Other Names: Jarczyk W. Academic Editor.; Kocinac L. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2013(2013)
• Publication Date: 2013-11-21
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2013/209256
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results.