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

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:

• Multi-patch
• HIV/AIDS
• migration
• basic reproduction number
• equilibrium

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34D20
• 34M04

Acknowledgments

The authors would like to thank the referees for their helpful suggestions that improved the presentation of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Sciences Foundation of China (No. 11971278), Shanxi Provincial Research and Development Program (No. 202102130501002) and Health Commission of Shanxi Province (2020XM18).