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 using probability Generating Functions (PGF). Models based on Mother to child transmission (MTCT) were developed, the expectations and variances of Susceptible (S) persons, Infected (I) persons, Treatment (T) and AIDS (A) cases were found. Sensitivity analysis was carried out to investigate the influence of key parameters on the spread of the disease. The result are presented graphically.
Keywords: HIV Transmission, Mother to Child Transmission and Treatment, Probability Generating Function, Stochastic compartmental model
