Abstract: This research provides a technical account of
estimating Transition Probability using Time-homogeneous Markov
Jump Process applying by South African HIV/AIDS data from the
Statistics South Africa. It employs Maximum Likelihood Estimator
(MLE) model to explore the possible influence of Transition
Probability of mortality cases in which case the data was based on
actual Statistics South Africa. This was conducted via an integrated
demographic and epidemiological model of South African HIV/AIDS
epidemic. The model was fitted to age-specific HIV prevalence data
and recorded death data using MLE model. Though the previous
model results suggest HIV in South Africa has declined and AIDS
mortality rates have declined since 2002 – 2013, in contrast, our
results differ evidently with the generally accepted HIV models
(Spectrum/EPP and ASSA2008) in South Africa. However, there is
the need for supplementary research to be conducted to enhance the
demographic parameters in the model and as well apply it to each of
the nine (9) provinces of South Africa.