DYNAMICS OF A STOCHASTIC HIV/AIDS MODEL WITH TREATMENT UNDER REGIME SWITCHING

Miaomiao Gao; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi; Bashir Ahmad

doi:10.3934/dcdsb.2021181

DYNAMICS OF A STOCHASTIC HIV/AIDS MODEL WITH TREATMENT UNDER REGIME SWITCHING

Miaomiao Gao
, Daqing Jiang
, Tasawar Hayat
, Ahmed Alsaedi
, Bashir Ahmad

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

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

6 Scopus citations

Abstract

This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.

Original language	English
Pages (from-to)	3177-3211
Number of pages	35
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	27
Issue number	6
DOIs	https://doi.org/10.3934/dcdsb.2021181
State	Published - Jun 2022
Externally published	Yes

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

Stochastic HIV/AIDS model
extinction
regime switching
stationary distribution
treatment

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10.3934/dcdsb.2021181

Cite this

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title = "DYNAMICS OF A STOCHASTIC HIV/AIDS MODEL WITH TREATMENT UNDER REGIME SWITCHING",

abstract = "This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.",

keywords = "Stochastic HIV/AIDS model, extinction, regime switching, stationary distribution, treatment",

author = "Miaomiao Gao and Daqing Jiang and Tasawar Hayat and Ahmed Alsaedi and Bashir Ahmad",

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doi = "10.3934/dcdsb.2021181",

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AU - Gao, Miaomiao

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

AU - Ahmad, Bashir

PY - 2022/6

Y1 - 2022/6

N2 - This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.

AB - This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.

KW - Stochastic HIV/AIDS model

KW - extinction

KW - regime switching

KW - stationary distribution

KW - treatment

UR - https://www.scopus.com/pages/publications/85131360808

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M3 - Article

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VL - 27

SP - 3177

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 6

ER -

DYNAMICS OF A STOCHASTIC HIV/AIDS MODEL WITH TREATMENT UNDER REGIME SWITCHING

Abstract

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Keywords

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