An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence Rate

This paper presents an investigation on the dynamics of an epidemic model with vital dynamics and a nonlinear incidence rate of saturated mass action as a function of the ratio of the number of the infectives to that of the susceptibles. The stabilities of the disease-free equilibrium and the endemi...

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Main Author:	Xinli Wang
Format:	Article
Language:	English
Published:	Hindawi Limited 2015-01-01
Series:	Discrete Dynamics in Nature and Society
Online Access:	http://dx.doi.org/10.1155/2015/720682

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spelling	doaj-0f667b20a0e04c16977898c9efe515e12020-11-24T23:49:41ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/720682720682An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence RateXinli Wang0College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaThis paper presents an investigation on the dynamics of an epidemic model with vital dynamics and a nonlinear incidence rate of saturated mass action as a function of the ratio of the number of the infectives to that of the susceptibles. The stabilities of the disease-free equilibrium and the endemic equilibrium are first studied. Under the assumption of nonexistence of periodic solution, the global dynamics of the model is established: either the number of infective individuals tends to zero as time evolves or it produces bistability in which there is a region such that the disease will persist if the initial position lies in the region and disappears if the initial position lies outside this region. Computer simulation shows such results.http://dx.doi.org/10.1155/2015/720682
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Xinli Wang
spellingShingle	Xinli Wang An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence Rate Discrete Dynamics in Nature and Society
author_facet	Xinli Wang
author_sort	Xinli Wang
title	An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence Rate
title_short	An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence Rate
title_full	An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence Rate
title_fullStr	An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence Rate
title_full_unstemmed	An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence Rate
title_sort	sirs epidemic model with vital dynamics and a ratio-dependent saturation incidence rate
publisher	Hindawi Limited
series	Discrete Dynamics in Nature and Society
issn	1026-0226 1607-887X
publishDate	2015-01-01
description	This paper presents an investigation on the dynamics of an epidemic model with vital dynamics and a nonlinear incidence rate of saturated mass action as a function of the ratio of the number of the infectives to that of the susceptibles. The stabilities of the disease-free equilibrium and the endemic equilibrium are first studied. Under the assumption of nonexistence of periodic solution, the global dynamics of the model is established: either the number of infective individuals tends to zero as time evolves or it produces bistability in which there is a region such that the disease will persist if the initial position lies in the region and disappears if the initial position lies outside this region. Computer simulation shows such results.
url	http://dx.doi.org/10.1155/2015/720682
work_keys_str_mv	AT xinliwang ansirsepidemicmodelwithvitaldynamicsandaratiodependentsaturationincidencerate AT xinliwang sirsepidemicmodelwithvitaldynamicsandaratiodependentsaturationincidencerate
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An SIRS Epidemic Model with Vital Dynamics and a Ratio-Dependent Saturation Incidence Rate

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