Mathematical modeling of HIV/AIDS dynamics with treatment and vertical transmission

This study proposes and analyzes a non-linear mathematical model for the dynamics of HIV/AIDS with treatment and vertical transmission. The equilibrium points of the model system are found and their stability is investigated. The model exhibits two equilibria namely, the disease-free and the endemic equilibrium. It is found that if the basic reproduction number RQ < 1, the disease-free equilibrium is always locally asymptotically stable and in such a case the endemic equilibrium does not exist. If > 1, a unique equilibrium exist which locally asymptotically stable and becomes globally asymptotically stable under certain conditions showing that the disease becomes endemic due to vertical transmission. By using stability theory and computer simulation, it is shown that by using treatment measures (ARVs) and by controlling the rate of vertical transmission, the spread of the disease can reduced significantly and also the equilibrium values of infective, pre-AIDS and AIDS population can be maintained at desired levels. A numerical study of the model is also used to investigate the influence of certain key parameters on the spread of the disease.