Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage

Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage

We extend the classical SIRS epidemic model incorporating media coverage from a deterministic framework to a stochastic differential equation (SDE) and focus on how environmental fluctuations of the contact coefficient affect the extinction of the disease. We give the conditions of existence of uniq...

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Main Authors: Liyan Wang, Huilin Huang, Ancha Xu, Weiming Wang
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/891765
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spelling doaj-90e905f137fe4b3b874a7dffb26ca1af2020-11-24T20:57:08ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/891765891765Stochastic Extinction in an SIRS Epidemic Model Incorporating Media CoverageLiyan Wang0Huilin Huang1Ancha Xu2Weiming Wang3College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaWe extend the classical SIRS epidemic model incorporating media coverage from a deterministic framework to a stochastic differential equation (SDE) and focus on how environmental fluctuations of the contact coefficient affect the extinction of the disease. We give the conditions of existence of unique positive solution and the stochastic extinction of the SDE model and discuss the exponential p-stability and global stability of the SDE model. One of the most interesting findings is that if the intensity of noise is large, then the disease is prone to extinction, which can provide us with some useful control strategies to regulate disease dynamics.http://dx.doi.org/10.1155/2013/891765
collection DOAJ
language English
format Article
sources DOAJ
author Liyan Wang
Huilin Huang
Ancha Xu
Weiming Wang
spellingShingle Liyan Wang
Huilin Huang
Ancha Xu
Weiming Wang
Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage
Abstract and Applied Analysis
author_facet Liyan Wang
Huilin Huang
Ancha Xu
Weiming Wang
author_sort Liyan Wang
title Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage
title_short Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage
title_full Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage
title_fullStr Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage
title_full_unstemmed Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage
title_sort stochastic extinction in an sirs epidemic model incorporating media coverage
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description We extend the classical SIRS epidemic model incorporating media coverage from a deterministic framework to a stochastic differential equation (SDE) and focus on how environmental fluctuations of the contact coefficient affect the extinction of the disease. We give the conditions of existence of unique positive solution and the stochastic extinction of the SDE model and discuss the exponential p-stability and global stability of the SDE model. One of the most interesting findings is that if the intensity of noise is large, then the disease is prone to extinction, which can provide us with some useful control strategies to regulate disease dynamics.
url http://dx.doi.org/10.1155/2013/891765
work_keys_str_mv AT liyanwang stochasticextinctioninansirsepidemicmodelincorporatingmediacoverage
AT huilinhuang stochasticextinctioninansirsepidemicmodelincorporatingmediacoverage
AT anchaxu stochasticextinctioninansirsepidemicmodelincorporatingmediacoverage
AT weimingwang stochasticextinctioninansirsepidemicmodelincorporatingmediacoverage
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