Complete global stability for an SIR epidemic model with delay - distributed or discrete
type: Item
instance of: scholarly article
title: Complete global stability for an SIR epidemic model with delay - distributed or discrete
zbMATH Open document ID: 1185.37209
author: C. Connell McCluskey
published in: Nonlinear Analysis. Real World Applications
publication date: 2010-01-12T00:00:00Z
review text: In modelling the transmission of an infectious disease, a common model structure involves dividing the population into susceptible, infectious and recovered individuals. If the immunity that is obtained upon recovery is permanent, then one gets an SIR model. In this paper the author considers SIR models with mass action incidence and constant recruitment. In Section 2 an SIR model with distributed delay is given. In Section 3, some results from the literature relating to earlier work on this model are given. Section 4 contains a proof of the global asymptotic stability of the endemic equilibrium for \({\mathfrak R}_0> 1\). In Section 5, an SIR model with discrete delay is presented and the endemic equilibrium is shown to be globally asymptotically stable for \({\mathfrak R}_0> 1\).
reviewed by: Marian Matłoka
Mathematics Subject Classification ID: 37N40
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 5656626
zbMATH Keywords: delay
zbMATH Keywords: distributed delay
zbMATH Keywords: global stability
zbMATH Keywords: Lyapunov functional
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2008.10.014
OpenAlex ID: W1993220987
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DOI: 10.1016/J.NONRWA.2008.10.014
description: scientific article; zbMATH DE number 5656626