Stability and Bogdanov-Takens bifurcation of an SIS epidemic model with saturated treatment function
type: Item
instance of: scholarly article
title: Stability and Bogdanov-Takens bifurcation of an SIS epidemic model with saturated treatment function
zbMATH Open document ID: 1394.92131
DOI: 10.1155/2015/745732
author: Yanju Xiao
author: Weipeng Zhang
author: Guifeng Deng
author: Zhehua Liu
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 6927145
zbMATH Keywords: Bogdanov-Takens bifurcation
zbMATH Keywords: Lyapunov coefficient
zbMATH Keywords: Hopf bifurcation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/745732
OpenAlex ID: W1997637719
Wikidata QID: Q59119793
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description: scientific article; zbMATH DE number 6927145