 Stability and bifurcation analysis of an SIR epidemic model with logistic growth and saturated treatmentJinhui Li, Zhidong Teng, Guangqing Wang, Long Zhang and Cheng Hu Chaos, Solitons & Fractals, 2017, vol. 99, issue C, 63-71 Abstract: In this paper, we introduce the saturated treatment and logistic growth rate into an SIR epidemic model with bilinear incidence. The treatment function is assumed to be a continuously differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large enough. Sufficient conditions for the existence and local stability of the disease-free and positive equilibria are established. And the existence of the stable limit cycles also is obtained. Moreover, by using the theory of bifurcations, it is shown that the model exhibits backward bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcations. Finally, the numerical examples are given to illustrate the theoretical results and obtain some additional interesting phenomena, involving double stable periodic solutions and stable limit cycles. Keywords: SIR epidemic model; Logistic growth; Saturated treatment; Equilibrium; Stability; Bifurcation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:99:y:2017:i:c:p:63-71 DOI: 10.1016/j.chaos.2017.03.047 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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