Background: Markov models are widely used in studying progression of chronic diseases using the time homogeneity approach. Relatively few studies use the time non-homogeneous approach to model the progression of HIV/AIDS based particularly in the use of viral load monitoring mainly due to fact that that viral load is expensive to measure frequently hence not readily available in the format required. Non-homogeneous models reveal the interval in which viral rebound occurs. Methods: This study compares the time-homogeneous Markov approach to the time nonhomogeneous approach in predicting HIV/AIDS progression. A piece-wise constant approach to non-homogeneous modelling is used. Results: This study reveals that a piece-wise constant Markov approach to non-homogeneous modelling which allows variation in transition rates within intervals [0,0.5) years and [0.5,∞) years is better for predicting HIV/AIDS progression compared to the time-homogeneous approach. Failure to combination antiretroviral therapy (cART) increases significantly the rate of viral rebound and deaths 6 months post treatment initiation. Conclusion: Hence, there is need to closely monitor the uptake of antiretroviral drugs in the first six months of treatment to increase the chances of survival for HIV/AIDS patients.