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...