Mathematical analysis of a sex-structured HIV/AIDS model with a discrete time delay

A sex-structured mathematical model for heterosexual transmission of HIV/AIDS with explicit incubation period is presented as a system of discrete delay differential equations. The epidemic threshold and equilibria for the model are determined and stabilities are examined. The disease-free equilibrium is shown to be locally and globally stable when the basic reproductive number R0R0 is less than unity. We use the Lyapunov functional approach to show that the endemic equilibrium is locally asymptotically stable. Further comprehensive qualitative analysis of the model including persistence and permanence are investigated.