Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence

Qun Liu; Daqing Jiang; Ningzhong Shi; Tasawar Hayat; Bashir Ahmad

doi:10.1016/j.physa.2017.02.028

Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence

Qun Liu
, Daqing Jiang
, Ningzhong Shi
, 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

60 Scopus citations

Abstract

In this paper, we consider a stochastic SEIR epidemic model with standard incidence. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution to the model. Our result does not depend on the positive endemic equilibrium E^∗ of the deterministic system, which improves the previous result to a greater extent. Moreover, we also establish sufficient conditions for extinction of the disease.

Original language	English
Pages (from-to)	58-69
Number of pages	12
Journal	Physica A: Statistical Mechanics and its Applications
Volume	476
DOIs	https://doi.org/10.1016/j.physa.2017.02.028
State	Published - 15 Jun 2017
Externally published	Yes

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

Extinction
Lyapunov function
Stationary distribution
Stochastic SEIR epidemic model

Access to Document

10.1016/j.physa.2017.02.028

Cite this

@article{89eda47dae2e445eab391b68f55d19a5,

title = "Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence",

abstract = "In this paper, we consider a stochastic SEIR epidemic model with standard incidence. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution to the model. Our result does not depend on the positive endemic equilibrium E∗ of the deterministic system, which improves the previous result to a greater extent. Moreover, we also establish sufficient conditions for extinction of the disease.",

keywords = "Extinction, Lyapunov function, Stationary distribution, Stochastic SEIR epidemic model",

author = "Qun Liu and Daqing Jiang and Ningzhong Shi and Tasawar Hayat and Bashir Ahmad",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

month = jun,

day = "15",

doi = "10.1016/j.physa.2017.02.028",

language = "English",

volume = "476",

pages = "58--69",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence

AU - Liu, Qun

AU - Jiang, Daqing

AU - Shi, Ningzhong

AU - Hayat, Tasawar

AU - Ahmad, Bashir

PY - 2017/6/15

Y1 - 2017/6/15

N2 - In this paper, we consider a stochastic SEIR epidemic model with standard incidence. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution to the model. Our result does not depend on the positive endemic equilibrium E∗ of the deterministic system, which improves the previous result to a greater extent. Moreover, we also establish sufficient conditions for extinction of the disease.

AB - In this paper, we consider a stochastic SEIR epidemic model with standard incidence. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution to the model. Our result does not depend on the positive endemic equilibrium E∗ of the deterministic system, which improves the previous result to a greater extent. Moreover, we also establish sufficient conditions for extinction of the disease.

KW - Extinction

KW - Lyapunov function

KW - Stationary distribution

KW - Stochastic SEIR epidemic model

UR - https://www.scopus.com/pages/publications/85014481371

U2 - 10.1016/j.physa.2017.02.028

DO - 10.1016/j.physa.2017.02.028

M3 - Article

AN - SCOPUS:85014481371

SN - 0378-4371

VL - 476

SP - 58

EP - 69

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence

Abstract

UN SDGs

Keywords

Access to Document

Other files and links

Fingerprint

Cite this