Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate

Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate

Based on some well-known SIR models, a revised nonautonomous SIR epidemic model with distributed delay and density-dependent birth rate was considered. Applying some classical analysis techniques for ordinary differential equations and the method proposed by Wang (2002), the threshold value for the...

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Main Authors: Li Yingke, Chen Liang, Wang Kai
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2011/350892
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spelling doaj-4edeb4c8178a402fa36da0be858504352020-11-24T22:31:17ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/350892350892Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth RateLi Yingke0Chen Liang1Wang Kai2College of Mathematics and Physics, Xinjiang Agricultural University, Urumqi 830052, ChinaDepartment of Mathematics, Changji College, Changji 831100, ChinaDepartment of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830054, ChinaBased on some well-known SIR models, a revised nonautonomous SIR epidemic model with distributed delay and density-dependent birth rate was considered. Applying some classical analysis techniques for ordinary differential equations and the method proposed by Wang (2002), the threshold value for the permanence and extinction of the model was obtained.http://dx.doi.org/10.1155/2011/350892
collection DOAJ
language English
format Article
sources DOAJ
author Li Yingke
Chen Liang
Wang Kai
spellingShingle Li Yingke
Chen Liang
Wang Kai
Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate
Discrete Dynamics in Nature and Society
author_facet Li Yingke
Chen Liang
Wang Kai
author_sort Li Yingke
title Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate
title_short Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate
title_full Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate
title_fullStr Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate
title_full_unstemmed Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate
title_sort permanence for a delayed nonautonomous sir epidemic model with density-dependent birth rate
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2011-01-01
description Based on some well-known SIR models, a revised nonautonomous SIR epidemic model with distributed delay and density-dependent birth rate was considered. Applying some classical analysis techniques for ordinary differential equations and the method proposed by Wang (2002), the threshold value for the permanence and extinction of the model was obtained.
url http://dx.doi.org/10.1155/2011/350892
work_keys_str_mv AT liyingke permanenceforadelayednonautonomoussirepidemicmodelwithdensitydependentbirthrate
AT chenliang permanenceforadelayednonautonomoussirepidemicmodelwithdensitydependentbirthrate
AT wangkai permanenceforadelayednonautonomoussirepidemicmodelwithdensitydependentbirthrate
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