Global stability of the endemic equilibrium of a discrete SIR epidemic model

The basic reproductive number [Formula: see text] of a discrete SIR epidemic model is defined and the dynamical behavior of the model is studied. It is proved that the disease free equilibrium is globally asymptotically stable if [Formula: see text], and the persistence of the model is obtained when...

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Autores principales: Ma, Xia, Zhou, Yicang, Cao, Hui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2013
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100002/
https://www.ncbi.nlm.nih.gov/pubmed/32226446
http://dx.doi.org/10.1186/1687-1847-2013-42
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author Ma, Xia
Zhou, Yicang
Cao, Hui
author_facet Ma, Xia
Zhou, Yicang
Cao, Hui
author_sort Ma, Xia
collection PubMed
description The basic reproductive number [Formula: see text] of a discrete SIR epidemic model is defined and the dynamical behavior of the model is studied. It is proved that the disease free equilibrium is globally asymptotically stable if [Formula: see text], and the persistence of the model is obtained when [Formula: see text]. The main attention is paid to the global stability of the endemic equilibrium. Sufficient conditions for the global stability of the endemic equilibrium are established by using the comparison principle. Numerical simulations are done to show our theoretical results and to demonstrate the complicated dynamics of the model. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/1687-1847-2013-42) contains supplementary material, which is available to authorized users.
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spelling pubmed-71000022020-03-27 Global stability of the endemic equilibrium of a discrete SIR epidemic model Ma, Xia Zhou, Yicang Cao, Hui Adv Differ Equ Research The basic reproductive number [Formula: see text] of a discrete SIR epidemic model is defined and the dynamical behavior of the model is studied. It is proved that the disease free equilibrium is globally asymptotically stable if [Formula: see text], and the persistence of the model is obtained when [Formula: see text]. The main attention is paid to the global stability of the endemic equilibrium. Sufficient conditions for the global stability of the endemic equilibrium are established by using the comparison principle. Numerical simulations are done to show our theoretical results and to demonstrate the complicated dynamics of the model. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/1687-1847-2013-42) contains supplementary material, which is available to authorized users. Springer International Publishing 2013-02-25 2013 /pmc/articles/PMC7100002/ /pubmed/32226446 http://dx.doi.org/10.1186/1687-1847-2013-42 Text en © Ma et al.; licensee Springer 2013 This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Open AccessThis article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research
Ma, Xia
Zhou, Yicang
Cao, Hui
Global stability of the endemic equilibrium of a discrete SIR epidemic model
title Global stability of the endemic equilibrium of a discrete SIR epidemic model
title_full Global stability of the endemic equilibrium of a discrete SIR epidemic model
title_fullStr Global stability of the endemic equilibrium of a discrete SIR epidemic model
title_full_unstemmed Global stability of the endemic equilibrium of a discrete SIR epidemic model
title_short Global stability of the endemic equilibrium of a discrete SIR epidemic model
title_sort global stability of the endemic equilibrium of a discrete sir epidemic model
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100002/
https://www.ncbi.nlm.nih.gov/pubmed/32226446
http://dx.doi.org/10.1186/1687-1847-2013-42
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AT caohui globalstabilityoftheendemicequilibriumofadiscretesirepidemicmodel

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