- This study is concerned with the mathematical modeling for human immunodeficiency virus (HIV) transmission epidemics. The mathematical models are specified by stochastic differential equations. The differential equations are solved by use of Generating Functions (GF).In the process of literature review, a conceptual framework is drawn which summarizes the literature on HIV / AIDS transmission epidemic models. Models based on Mother to child transmission (MTCT) (age group 0-5 years), Heterosexual transmission (age group 15 and more years) and combined case (incorporating all groups and the two modes of transmission) are developed and the expectations and variances of Susceptible (S) persons, Infected (I) persons and AIDS cases found. It is shown from the combined model that MTCT and Heterosexual models are special cases of the combined model. General aspects of modeling HIV/AIDS are described in chapter 1, Chapter 2 focuses on the literature review. MTCT model.is formulated in chapter 3. Heterosexual model is developed in chapter 4, Chapter 5 focuses on the development of the Combined model. Chapter 6 concludes the study.