 This paper presents a numerical analysis of the mathematical model of HIV, AIDS disease transmission. It compares the results of the proposed scheme with those of other classical schemes that exist in the literature. The proposed scheme provides more accurate results with a larger step size than the RK4 method with a smaller step size. Additionally, it implements the method to the extended model by introducing a treatment rate and shows the impact of various non-linear source terms on the generation of new cells. Furthermore, the basic reproduction number and the Ralph Hurwitz criterion are used to assess the stability of disease-free and unique endemic equilibrium states of the HIV model. This article was authored by Atala, Kamil Zeb, Elias Khan, and others.