- This study is concerned with the mathematical modeling for human immunodeficiency virus (HIV) transmission epidemics. The mathematical models are specified by stochastic differential equations that are solved by use of Generating Functions (GF). 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) were developed and the expectations and variances of Susceptible (S) persons, Infected (I) persons and AIDS cases were found. The S1" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; font-size: 14px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(51, 51, 51); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; position: relative;">11(t) Susceptible model produces a constant expectation and increasing variance. It was shown that Mother to Child transimission and Heterosexual models are special cases of the Combined model.