Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate

Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate

In this paper, we consider a stochastic SIQR epidemic model with saturated incidence rate. By constructing a proper Lyapunov function, we obtain the existence and uniqueness of positive solution for this SIQR model. Furthermore, we study the dynamical properties of this stochastic SIQR model; that i...

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Main Authors: Qiuhua Zhang, Kai Zhou
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2019/3575410
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spelling doaj-7a305316d0d64de58974890aae4f92a82020-11-25T01:21:16ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472019-01-01201910.1155/2019/35754103575410Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence RateQiuhua Zhang0Kai Zhou1School of Mathematics and Computers, Chizhou University, Chizhou 247000, ChinaSchool of Mathematics and Computers, Chizhou University, Chizhou 247000, ChinaIn this paper, we consider a stochastic SIQR epidemic model with saturated incidence rate. By constructing a proper Lyapunov function, we obtain the existence and uniqueness of positive solution for this SIQR model. Furthermore, we study the dynamical properties of this stochastic SIQR model; that is, (i) we establish the sufficient condition for the existence of ergodic stationary distribution of the model; (ii) we obtain the extinction of the disease under some conditions. At last, numerical simulations are introduced to illustrate our theoretical results.http://dx.doi.org/10.1155/2019/3575410
collection DOAJ
language English
format Article
sources DOAJ
author Qiuhua Zhang
Kai Zhou
spellingShingle Qiuhua Zhang
Kai Zhou
Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate
Mathematical Problems in Engineering
author_facet Qiuhua Zhang
Kai Zhou
author_sort Qiuhua Zhang
title Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate
title_short Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate
title_full Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate
title_fullStr Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate
title_full_unstemmed Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate
title_sort stationary distribution and extinction of a stochastic siqr model with saturated incidence rate
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2019-01-01
description In this paper, we consider a stochastic SIQR epidemic model with saturated incidence rate. By constructing a proper Lyapunov function, we obtain the existence and uniqueness of positive solution for this SIQR model. Furthermore, we study the dynamical properties of this stochastic SIQR model; that is, (i) we establish the sufficient condition for the existence of ergodic stationary distribution of the model; (ii) we obtain the extinction of the disease under some conditions. At last, numerical simulations are introduced to illustrate our theoretical results.
url http://dx.doi.org/10.1155/2019/3575410
work_keys_str_mv AT qiuhuazhang stationarydistributionandextinctionofastochasticsiqrmodelwithsaturatedincidencerate
AT kaizhou stationarydistributionandextinctionofastochasticsiqrmodelwithsaturatedincidencerate
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