Mathematical Model of HIV/AIDS with Two Different Stages of Infection Subpopulation and Its Stability Analysis

We propose mathematical model of HIV/AIDS with two different stages of infection subpopulation. The proposed model is more realistic since it establishes the compartment diagram based on data from the Indonesian Ministry of Health. The model consists of six compartments (susceptible, infected with and without treatment, AIDS, treatment, and recovered sub populations). We analyzed the model by proving the positivity and boundedness of the models solutions. Furthermore, we analyzed local and global stability of the solutions determined by the basic reproduction number as a threshold of disease transmission. The disease-free and endemic equilibrium points are locally asymptotically stable when R-0 < 1 and R-0 > 1 respectively. For global stability, we constructed the Lyapunov function. The results indicate that the disease-free equilibrium point is globally asymptotically stable when R-0 < 1 and that the endemic equilibrium point is globally asymptotically stable when R-0 > 1. We conducted numerical simulation to support the analytical results.