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Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence
In this paper, a class of discrete SEIRS epidemic models with general nonlinear incidence is investigated. Particularly, a discrete SEIRS epidemic model with standard incidence is also considered. The positivity and boundedness of solutions with positive initial conditions are obtained. It is shown...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2016
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100848/ https://www.ncbi.nlm.nih.gov/pubmed/32226447 http://dx.doi.org/10.1186/s13662-016-0846-y |
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author | Fan, Xiaolin Wang, Lei Teng, Zhidong |
author_facet | Fan, Xiaolin Wang, Lei Teng, Zhidong |
author_sort | Fan, Xiaolin |
collection | PubMed |
description | In this paper, a class of discrete SEIRS epidemic models with general nonlinear incidence is investigated. Particularly, a discrete SEIRS epidemic model with standard incidence is also considered. The positivity and boundedness of solutions with positive initial conditions are obtained. It is shown that if the basic reproduction number [Formula: see text] , then disease-free equilibrium is globally attractive, and if [Formula: see text] , then the disease is permanent. When the model degenerates into SEIR model, it is proved that if [Formula: see text] , then the model has a unique endemic equilibrium, which is globally attractive. Furthermore, the numerical examples verify an important open problem that when [Formula: see text] , the endemic equilibrium of general SEIRS models is also globally attractive. |
format | Online Article Text |
id | pubmed-7100848 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-71008482020-03-27 Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence Fan, Xiaolin Wang, Lei Teng, Zhidong Adv Differ Equ Research In this paper, a class of discrete SEIRS epidemic models with general nonlinear incidence is investigated. Particularly, a discrete SEIRS epidemic model with standard incidence is also considered. The positivity and boundedness of solutions with positive initial conditions are obtained. It is shown that if the basic reproduction number [Formula: see text] , then disease-free equilibrium is globally attractive, and if [Formula: see text] , then the disease is permanent. When the model degenerates into SEIR model, it is proved that if [Formula: see text] , then the model has a unique endemic equilibrium, which is globally attractive. Furthermore, the numerical examples verify an important open problem that when [Formula: see text] , the endemic equilibrium of general SEIRS models is also globally attractive. Springer International Publishing 2016-05-06 2016 /pmc/articles/PMC7100848/ /pubmed/32226447 http://dx.doi.org/10.1186/s13662-016-0846-y Text en © Fan et al. 2016 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Research Fan, Xiaolin Wang, Lei Teng, Zhidong Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence |
title | Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence |
title_full | Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence |
title_fullStr | Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence |
title_full_unstemmed | Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence |
title_short | Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence |
title_sort | global dynamics for a class of discrete seirs epidemic models with general nonlinear incidence |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100848/ https://www.ncbi.nlm.nih.gov/pubmed/32226447 http://dx.doi.org/10.1186/s13662-016-0846-y |
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