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

Qun Liu; Daqing Jiang; Tasawar Hayat; Bashir Ahmad

doi:10.1080/07362994.2017.1378897

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

Qun Liu
, Daqing Jiang
, Tasawar Hayat
, Bashir Ahmad

Northeast Normal University
Yulin Normal University
Faculty of Sciences, King Abdulaziz University
China University of Petroleum (East China)
Quaid-I-Azam University

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

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.

Original language	English
Pages (from-to)	138-151
Number of pages	14
Journal	Stochastic Analysis and Applications
Volume	36
Issue number	1
DOIs	https://doi.org/10.1080/07362994.2017.1378897
State	Published - 2 Jan 2018
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Lyapunov function
Stochastic SIRI epidemic model
extinction
stationary distribution and ergodicity

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10.1080/07362994.2017.1378897

Cite this

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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.",

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AU - Hayat, Tasawar

AU - Ahmad, Bashir

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AB - 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.

KW - Lyapunov function

KW - Stochastic SIRI epidemic model

KW - extinction

KW - stationary distribution and ergodicity

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

Abstract

UN SDGs

Keywords

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