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In HIV/AIDS treatment, there is need for physician to use realistic and interpretable tools in their daily medical care of patients. In this work, a Homogenous Semi-Markov Model (HSMM) in discrete time is introduced and defined. The HIV/AIDS model considered is based on CD4 count levels and this multistate model is made of four immunological states. A large number of results have been obtained including the following conditional probabilities: an infected patient will be in state j after a time t, given that the patient entered at a time 0 (starting time) in state i; that he/she will continue to remain in the starting state up to time t; that he/she reach stage j of the disease in the next transition, if the previous state was i and no state change occurred up to time t. The result of the expected duration by means of renewal time in a state shows that an infected patient spends smaller time in AIDS full blown stage than other immunological stages. This model when compared with to the most common epidemiological data analyses, has several advantages discussed in this work.

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Alao olalere is a young researcher. He obtained his Bachelor degree in statistics and completed his M.sc thesis in statistics with specialization in stochastics processes in the year 2003 and 2009 respectively. He has co-author other books including "Pathway to Academic Success". He is happily married and blessed with children.

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