Abstract: In this study, we examined, the Susceptibles-Infectives-Removed/Recovered, (SIR) epidemic model and applied it to horizontal transmission of HIV/AIDS in a homogeneous mixing population. with additional assumption that AIDS virus does not kill instead; AIDS-infectives are removed from circulation until death by non disease induced. Also the stability of the equilibrium points are examined via the basic reproductive number of the infection and trace-determinant condition of the Jacobian matrix at the equilibrium point, for a system of non-linear differential equation. The threshold conditions on the model parameters, which allows stability of the disease-free equilibrium and the endemic equilibrium points are derived and their biological interpretations given.