Stability Analysis of a Delayed HIV/AIDS Epidemic Model with Treatment and Vertical Transmission

Abstract

A delayed HI V/A IDS epidemic model with treatment and vertical transmission is investigated. The model allows some infected individuals to move from the symptomatic phase to the asymptomatic phase; next generation of infected individuals may be infected and it will take them some time to get maturity and infect others. Mathematical analysis shows that the global dynamics of the spread of the HIV/AIDS are completely determined by the basic reproduction number R 0 for our model. If R 0 < 1 then disease free equilibrium is globally asymptotically stable, whereas the unique infected equilibrium is globally asymptotically stable if R 0 > 1.