Mathematical modelling of HIV/AIDS with some government intervention strategies: the case study of Tanzania

A mathematical model for the transmission dynamics of HIV /AIDS with High Active Antiretroviral Therapy (HAART) and testing and counseling as interven¬tion strategies in a population is formulated and analyzed. The analysis of the model has been done qualitatively so as to investigate the existence and stability of equilibria. The global stability of the disease free equilibrium is investigated by using the center manifold theory and conditions for the global stability are derived by using the comparison method. The disease-free is shown to be locally asymptotically stable when the threshold quantity defined as the number of new invectives individual in a completely susceptible population is less than unity. By using the center manifold theory, the HIV/AIDS model is shown to have a unique and locally asymptotically stable endemic equilibrium when the thresh¬old quantity, SRo is greater than unity. By analyzing the associated reproduction number, it is shown that the HAART, testing and counseling intervention strate¬gies, reduce the rate of transmission of HIV infection. Numerical simulations of the model were carried out to assess the impact of HAART, testing and counseling strategies. It is observed that, before interven¬tions the threshold quantity, is greater than unity, meaning the disease exists but after intervention, threshold quantity, $Ro was reduced below unity. Prom the results of the numerical simulations it is concluded that the intervention strate¬gies reduce the rate of transmission of the HIV infection as well as the new cases in a population.