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 R0 and prove that if R0<1, the disease-free equilibrium is globally asymptotically stable. If R0>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.