Stability analysis of an HIV/AIDS epidemic model with sexual transmission in a patchy environment

Juping Zhang; Xueyan Ma; Zhen Jin

doi:10.1080/17513758.2023.2227216

Stability analysis of an HIV/AIDS epidemic model with sexual transmission in a patchy environment

J Biol Dyn. 2023 Dec;17(1):2227216. doi: 10.1080/17513758.2023.2227216.

Authors

Juping Zhang^{1

2}, Xueyan Ma^{1

2}, Zhen Jin^{1

2}

Affiliations

¹ Complex Systems Research Center, Shanxi University, Taiyuan, People's Republic of China.
² Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan, People's Republic of China.

PMID: 37377414
DOI: 10.1080/17513758.2023.2227216

Abstract

A multi-patch HIV/AIDS model with heterosexual transmission is formulated to investigate the impact of population migration on the spread of HIV/AIDS. We derive the basic reproduction number $R_{0}$ and prove that if $R_{0} < 1$ , the disease-free equilibrium is globally asymptotically stable. If $R_{0} > 1$ and certain conditions are satisfied, the endemic equilibrium is globally asymptotically stable. We apply the model to two patches and conduct numerical simulations. If HIV/AIDS becomes extinct in each patch when two patches are isolated, the disease remains extinct in two patches when the population migration occurs; if HIV/AIDS spreads in each patch when two patches are isolated, the disease remains persistent in two patches when the population migration occurs; if the disease disappears in one patch and spreads in the other patch when they are isolated, the disease can spread or disappear in two patches if migration rates of individuals are suitably chosen.

Keywords: 34D20; 34M04; HIV/AIDS; Multi-patch; basic reproduction number; equilibrium; migration.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Basic Reproduction Number
Epidemics*
HIV Infections* / epidemiology
Humans
Models, Biological