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(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
