The medical community can get a deeper understanding of the physiological and pathological processes occurring within the human body through mathematical modeling, which can also lead to more precise and dependable medical diagnoses and predictions. There formerly was no effective medication available to save newborns from HIV-affected pregnancies. We now have the necessary medical care to save babies who do not have HIV. The HIV pandemic model is developed mathematically using the ideas of difference equations. We took treatment effects into account when building the mathematical model. For our model, we computed both endemic and disease-free equilibrium points. An effective reproduction number for the model is computed using the next-generation matrix. We further investigate boundedness and non-negativity. We also proved that HIV-free equilibrium is locally asymptotic when the basic reproduction number, \(R_{0}\) , is less than the unity. In the HIV epidemic model, its outcomes are analyzed by way of Matrix Laboratory.