Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model

We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of...

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Main Authors:	Zhijian Wei, Meitao Le
Format:	Article
Language:	English
Published:	Hindawi Limited 2015-01-01
Series:	Discrete Dynamics in Nature and Society
Online Access:	http://dx.doi.org/10.1155/2015/434537

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spelling	doaj-4eb92fbbb124430199c01c8635a0f6122020-11-24T22:43:08ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/434537434537Existence and Convergence of the Positive Solutions of a Discrete Epidemic ModelZhijian Wei0Meitao Le1College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, ChinaCollege of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, ChinaWe consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations. The obtained results are new and they complement previously known results.http://dx.doi.org/10.1155/2015/434537
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Zhijian Wei Meitao Le
spellingShingle	Zhijian Wei Meitao Le Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model Discrete Dynamics in Nature and Society
author_facet	Zhijian Wei Meitao Le
author_sort	Zhijian Wei
title	Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model
title_short	Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model
title_full	Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model
title_fullStr	Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model
title_full_unstemmed	Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model
title_sort	existence and convergence of the positive solutions of a discrete epidemic model
publisher	Hindawi Limited
series	Discrete Dynamics in Nature and Society
issn	1026-0226 1607-887X
publishDate	2015-01-01
description	We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations. The obtained results are new and they complement previously known results.
url	http://dx.doi.org/10.1155/2015/434537
work_keys_str_mv	AT zhijianwei existenceandconvergenceofthepositivesolutionsofadiscreteepidemicmodel AT meitaole existenceandconvergenceofthepositivesolutionsofadiscreteepidemicmodel
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Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model

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