Stationary distribution of a stochastic cholera model between communities linked by migration

Qun Liu; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi; Bashir Ahmad

doi:10.1016/j.amc.2019.125021

Stationary distribution of a stochastic cholera model between communities linked by migration

Qun Liu
, Daqing Jiang
, Tasawar Hayat
, Ahmed Alsaedi
, Bashir Ahmad

Northeast Normal University
China University of Petroleum (East China)
King Abdulaziz University
Quaid-I-Azam University

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

12 Scopus citations

Abstract

In this paper, we develop and study a stochastic cholera model between communities linked by migration. Firstly, we show that there exists a unique global positive solution of the considered system with any positive initial value. Then by using the stochastic Lyapunov analysis method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Our result shows that the migration and the small white noise are not beneficial for eliminating cholera. Finally, some examples together with numerical simulations are introduced to support the theoretical result.

Original language	English
Article number	125021
Journal	Applied Mathematics and Computation
Volume	373
DOIs	https://doi.org/10.1016/j.amc.2019.125021
State	Published - 15 May 2020
Externally published	Yes

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

Cholera model
Ergodicity
Migration
Stationary distribution

Access to Document

10.1016/j.amc.2019.125021

Cite this

@article{9857b03e8ed54613bc3754a2000dec8e,

title = "Stationary distribution of a stochastic cholera model between communities linked by migration",

abstract = "In this paper, we develop and study a stochastic cholera model between communities linked by migration. Firstly, we show that there exists a unique global positive solution of the considered system with any positive initial value. Then by using the stochastic Lyapunov analysis method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Our result shows that the migration and the small white noise are not beneficial for eliminating cholera. Finally, some examples together with numerical simulations are introduced to support the theoretical result.",

keywords = "Cholera model, Ergodicity, Migration, Stationary distribution",

author = "Qun Liu and Daqing Jiang and Tasawar Hayat and Ahmed Alsaedi and Bashir Ahmad",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

month = may,

day = "15",

doi = "10.1016/j.amc.2019.125021",

language = "English",

volume = "373",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Stationary distribution of a stochastic cholera model between communities linked by migration

AU - Liu, Qun

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

AU - Ahmad, Bashir

PY - 2020/5/15

Y1 - 2020/5/15

N2 - In this paper, we develop and study a stochastic cholera model between communities linked by migration. Firstly, we show that there exists a unique global positive solution of the considered system with any positive initial value. Then by using the stochastic Lyapunov analysis method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Our result shows that the migration and the small white noise are not beneficial for eliminating cholera. Finally, some examples together with numerical simulations are introduced to support the theoretical result.

AB - In this paper, we develop and study a stochastic cholera model between communities linked by migration. Firstly, we show that there exists a unique global positive solution of the considered system with any positive initial value. Then by using the stochastic Lyapunov analysis method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Our result shows that the migration and the small white noise are not beneficial for eliminating cholera. Finally, some examples together with numerical simulations are introduced to support the theoretical result.

KW - Cholera model

KW - Ergodicity

KW - Migration

KW - Stationary distribution

UR - https://www.scopus.com/pages/publications/85077738885

U2 - 10.1016/j.amc.2019.125021

DO - 10.1016/j.amc.2019.125021

M3 - Article

AN - SCOPUS:85077738885

SN - 0096-3003

VL - 373

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 125021

ER -

Stationary distribution of a stochastic cholera model between communities linked by migration

Abstract

UN SDGs

Keywords

Access to Document

Other files and links

Fingerprint

Cite this