We propose mathematical model of HIV/AIDS with two different stages of infection and susceptible subpopulations. The two stages in infection subpopulation are an HIV-positive with consuming ARV such that this subpopulation can survive longer and an HIV-positive without consuming ARV stage. The susceptible subpopulation is divided into two, uneducated and educated susceptible subpopulations. The compartment diagram of the model can be seen in the Figure 1

Figure 1. The compartment diagram of HIV/AIDS Model.

where represents the number of uneducated susceptible individuals; represents the number of educated susceptible individuals; represents the number of HIV-positive individuals with consuming ARV such that this subpopulation can survive longer and represents the number of HIV-positive individuals without consuming ARV; represents the number of individuals with full-blown AIDS not receiving treatment; represents the number of individuals who are receiving ARV treatment; represents the number of individuals who change their sexual habits and maintain the habits for the rest of their lives. The transmission coefficients from educated and uneducated subpopulations to be infection stages are where ( and > and ). In this research, we consider the case of and are zero.

We investigate local stability of the model solutions according to the basic reproduction number as a threshold of disease transmission. The disease-free and endemic equilibrium points are locally asymptotically stable when and respectively. To support the analytical results, numerical simulation are conducted.