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Stochastic Analysis and Applications Volume 36, 2018 - Issue 1
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Original Articles

Stationary distribution and extinction of a stochastic SIRI epidemic model with relapse

Qun LiuSchool of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, Jilin, P.R. China;School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, Guangxi, P.R. China
,
Daqing JiangSchool of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, Jilin, P.R. China;Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;College of Science, China University of Petroleum (East China), Qingdao, Shandong, P.R. ChinaCorrespondence[email protected]
,
Tasawar HayatNonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
&
Bashir AhmadNonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
Pages 138-151 | Received 18 Mar 2017, Accepted 09 Sep 2017, Published online: 02 Jan 2018
 
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ABSTRACT

In this paper, we study the dynamics of a stochastic Susceptible-Infective-Removed-Infective (SIRI) epidemic model with relapse. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Moreover, sufficient conditions for extinction of the disease are also obtained.

MATHEMATICS SUBJECT CLASSIFICATION:

Funding

This work was supported by NSFC of China Grant No. 11371085, the Fundamental Research Funds for the Central Universities (No. 15CX08011A), 2016GXNSFBA380006, and KY2016YB370.

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