Permanence of a delayed SIR epidemic model with density dependent birth rate
type: Item
instance of: scholarly article
title: Permanence of a delayed SIR epidemic model with density dependent birth rate
zbMATH Open document ID: 1117.34310
author: Mei Song
author: Wanbiao Ma
author: Yasuhiro Takeuchi
published in: Journal of Computational and Applied Mathematics
publication date: 2007-03-08T00:00:00Z
review text: The authors consider the following SIR epidemic model with time delay \[ \frac{dS(t)}{dt}=-\beta S(t)I(t-h)-\mu _1S(t)+b\left( 1-\beta _1\frac{N(t)}{ 1+N(t)}\right), \] \[ \frac{dI(t)}{dt}=\beta S(t)I(t-h)-\mu _2I(t)-\lambda I(t),\quad \frac{dR(t)}{dt}=\lambda I(t)-\mu _3R(t), \] where \(S(t),\) \(I(t)\) and \(R(t)\) denote the numbers of susceptible members to the disease, of infective members and of members who have been removed from the possibility of infection through full immunity, respectively. Some permanence results are established when the positive equilibrium exists.
reviewed by: Haifeng Huo
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 5131571
zbMATH Keywords: SIR epidemic model
zbMATH Keywords: time delay
zbMATH Keywords: permanence
MaRDI profile type: Publication
full work available at URL: j.cam.2005.12.039
OpenAlex ID: W2094003690
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DOI: 10.1016/J.CAM.2005.12.039
description: scientific article; zbMATH DE number 5131571