101. Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function
- Author
-
Guifeng Deng, Zhehua Liu, Weipeng Zhang, and Yanju Xiao
- Subjects
Lyapunov function ,Hopf bifurcation ,Article Subject ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,General Engineering ,Function (mathematics) ,Bifurcation diagram ,lcsh:QA1-939 ,symbols.namesake ,Exponential stability ,lcsh:TA1-2040 ,symbols ,Bogdanov–Takens bifurcation ,Epidemic model ,lcsh:Engineering (General). Civil engineering (General) ,Bifurcation ,Mathematics - Abstract
This paper introduces the global dynamics of an SIS model with bilinear incidence rate and saturated treatment function. The treatment function is a continuous and differential function which shows the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger. Sufficient conditions for the existence and global asymptotic stability of the disease-free and endemic equilibria are given in this paper. The first Lyapunov coefficient is computed to determine various types of Hopf bifurcation, such as subcritical or supercritical. By some complex algebra, the Bogdanov-Takens normal form and the three types of bifurcation curves are derived. Finally, mathematical analysis and numerical simulations are given to support our theoretical results.
- Published
- 2015