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Global dynamics for an SIR patchy model with susceptibles dispersal
An [Formula: see text] epidemiological model with suscptibles dispersal between two patches is addressed and discussed. The basic reproduction numbers [Formula: see text] and [Formula: see text] are defined as the threshold parameters. It shows that if both [Formula: see text] and [Formula: see text...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2012
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7099918/ https://www.ncbi.nlm.nih.gov/pubmed/32226445 http://dx.doi.org/10.1186/1687-1847-2012-131 |
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author | Liu, Luju Cai, Weiyun Wu, Yusen |
author_facet | Liu, Luju Cai, Weiyun Wu, Yusen |
author_sort | Liu, Luju |
collection | PubMed |
description | An [Formula: see text] epidemiological model with suscptibles dispersal between two patches is addressed and discussed. The basic reproduction numbers [Formula: see text] and [Formula: see text] are defined as the threshold parameters. It shows that if both [Formula: see text] and [Formula: see text] are below unity, the disease-free equilibrium is shown to be globally asymptotically stable by using the comparison principle of the cooperative systems. If [Formula: see text] is above unity and [Formula: see text] is below unity, the disease persists in the first patch provided [Formula: see text]. If [Formula: see text] is above unity, [Formula: see text] is below unity, and [Formula: see text], the disease persists in the second patch. And if [Formula: see text] and [Formula: see text] are above unity, and further [Formula: see text] and [Formula: see text] are satisfied, the unique endemic equilibrium is globally asymptotically stable by constructing the Lyapunov function. Furthermore, it follows that the susceptibles dispersal in the population does not alter the qualitative behavior of the epidemiological model. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/1687-1847-2012-131) contains supplementary material, which is available to authorized users. |
format | Online Article Text |
id | pubmed-7099918 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2012 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-70999182020-03-27 Global dynamics for an SIR patchy model with susceptibles dispersal Liu, Luju Cai, Weiyun Wu, Yusen Adv Differ Equ Research An [Formula: see text] epidemiological model with suscptibles dispersal between two patches is addressed and discussed. The basic reproduction numbers [Formula: see text] and [Formula: see text] are defined as the threshold parameters. It shows that if both [Formula: see text] and [Formula: see text] are below unity, the disease-free equilibrium is shown to be globally asymptotically stable by using the comparison principle of the cooperative systems. If [Formula: see text] is above unity and [Formula: see text] is below unity, the disease persists in the first patch provided [Formula: see text]. If [Formula: see text] is above unity, [Formula: see text] is below unity, and [Formula: see text], the disease persists in the second patch. And if [Formula: see text] and [Formula: see text] are above unity, and further [Formula: see text] and [Formula: see text] are satisfied, the unique endemic equilibrium is globally asymptotically stable by constructing the Lyapunov function. Furthermore, it follows that the susceptibles dispersal in the population does not alter the qualitative behavior of the epidemiological model. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/1687-1847-2012-131) contains supplementary material, which is available to authorized users. Springer International Publishing 2012-08-01 2012 /pmc/articles/PMC7099918/ /pubmed/32226445 http://dx.doi.org/10.1186/1687-1847-2012-131 Text en © Liu et al.; licensee Springer 2012 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 Liu, Luju Cai, Weiyun Wu, Yusen Global dynamics for an SIR patchy model with susceptibles dispersal |
title | Global dynamics for an SIR patchy model with susceptibles dispersal |
title_full | Global dynamics for an SIR patchy model with susceptibles dispersal |
title_fullStr | Global dynamics for an SIR patchy model with susceptibles dispersal |
title_full_unstemmed | Global dynamics for an SIR patchy model with susceptibles dispersal |
title_short | Global dynamics for an SIR patchy model with susceptibles dispersal |
title_sort | global dynamics for an sir patchy model with susceptibles dispersal |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7099918/ https://www.ncbi.nlm.nih.gov/pubmed/32226445 http://dx.doi.org/10.1186/1687-1847-2012-131 |
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