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

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.

Automated summary

A multi-patch HIV/AIDS model with heterosexual transmission is used to study the impact of population migration. The basic reproduction number R0 is derived and it is proven that if R0 < 1, the disease-free equilibrium is globally asymptotically stable. If R0 > 1 and certain conditions are met, the endemic equilibrium is globally asymptotically stable. The model is applied to two patches and numerical simulations are conducted to analyze the spread of HIV/AIDS when population migration occurs.