Backward bifurcation in simple SIS model
type: Item
instance of: scholarly article
title: Backward bifurcation in simple SIS model
zbMATH Open document ID: 1189.34086
author: Zhanwei Wang
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2009-11-13T00:00:00Z
review text: A simple epidemic model of SIS-type is investigated, where the treatment of infected persons is proportional to the infection rate only up to a given value, and is held constant for higher infection rates. The author presents a qualitative analysis in two steps: First, when the disease-induced death rate is zero, and, secondly, when this rate is positive. In the first case, Thieme's theory of asymptotically autonomous systems is used to reduce the (S,I)-system to a single nonsmooth differential equation which easily admits the investigation of the equilibria and their stability as a function of an essential parameter. The second case may not be reduced to a one-dimensional problem. Nevertheless, a rather complete analysis is carried out in the (S,I)-plane. It yields the existence of multiple endemic equilibria, their position and, in particular, their backward bifurcation for certain parameter values. Moreover, results are obtained concerning Hopf bifurcation and the nonexistence of periodic orbits.
reviewed by: Josef Hainzl
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5632898
zbMATH Keywords: epidemiology
zbMATH Keywords: SIS-model
zbMATH Keywords: backward bifurcation
zbMATH Keywords: bistability
zbMATH Keywords: limit cycle
MaRDI profile type: Publication
full work available at URL: s10255-006-6160-9
OpenAlex ID: W2151503487
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DOI: 10.1007/S10255-006-6160-9
description: scientific article; zbMATH DE number 5632898