Dynamics of a stochastic tuberculosis transmission model with treatment at home

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

doi:10.1080/07362994.2020.1753539

Dynamics of a stochastic tuberculosis transmission model with treatment at home

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

2 Scopus citations

Abstract

In this paper, we consider a stochastic tuberculosis model with two kinds of treatments, that is, treatment at home and treatment in hospital. Firstly, we obtain sufficient conditions for extinction and persistence in the mean of the diseases, then in the case of persistence, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The theoretical results show that large white noise is beneficial for eliminating TB endemic while small white noise is not.

Original language	English
Pages (from-to)	979-1000
Number of pages	22
Journal	Stochastic Analysis and Applications
Volume	38
Issue number	6
DOIs	https://doi.org/10.1080/07362994.2020.1753539
State	Published - 1 Nov 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

Tuberculosis
extinction
persistence in the mean
stationary distribution and ergodicity
treatment

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10.1080/07362994.2020.1753539

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title = "Dynamics of a stochastic tuberculosis transmission model with treatment at home",

abstract = "In this paper, we consider a stochastic tuberculosis model with two kinds of treatments, that is, treatment at home and treatment in hospital. Firstly, we obtain sufficient conditions for extinction and persistence in the mean of the diseases, then in the case of persistence, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The theoretical results show that large white noise is beneficial for eliminating TB endemic while small white noise is not.",

keywords = "Tuberculosis, extinction, persistence in the mean, stationary distribution and ergodicity, treatment",

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

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TY - JOUR

T1 - Dynamics of a stochastic tuberculosis transmission model with treatment at home

AU - Liu, Qun

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

AU - Ahmad, Bashir

PY - 2020/11/1

Y1 - 2020/11/1

N2 - In this paper, we consider a stochastic tuberculosis model with two kinds of treatments, that is, treatment at home and treatment in hospital. Firstly, we obtain sufficient conditions for extinction and persistence in the mean of the diseases, then in the case of persistence, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The theoretical results show that large white noise is beneficial for eliminating TB endemic while small white noise is not.

AB - In this paper, we consider a stochastic tuberculosis model with two kinds of treatments, that is, treatment at home and treatment in hospital. Firstly, we obtain sufficient conditions for extinction and persistence in the mean of the diseases, then in the case of persistence, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The theoretical results show that large white noise is beneficial for eliminating TB endemic while small white noise is not.

KW - Tuberculosis

KW - extinction

KW - persistence in the mean

KW - stationary distribution and ergodicity

KW - treatment

UR - https://www.scopus.com/pages/publications/85083842575

U2 - 10.1080/07362994.2020.1753539

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M3 - Article

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EP - 1000

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 6

ER -

Dynamics of a stochastic tuberculosis transmission model with treatment at home

Abstract

UN SDGs

Keywords

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