Applied Journal of Physical Science

Semi-Markov model in discrete state and time to study the trajection among the various defined HIV/AIDs stages has been presented in this paper. The model was used to determine the staging of HIV- infected clients reported at heart-to-heart clinic of General Hospital Minna, Niger State, Nigeria for a period of 10 years. The result shows that there is no transition from asymptomatic stage of HIV to late/advance AIDs such that φ₁₄ (n) = 0; which led to gradual increment in the graphs of interval transition probabilities for all n ∈ N. The study shows that there are some increments in the transition probabilities from stages 2, 3 and 4 to stage 1 from about 0.05745, 0.01055 and 0.00379 in the first month (n = 1) to about 0.37163, 0.17821 and 0.05862 in the forty four months (n = 44) and in the forty five months (n = 45) respectively. From the virtual transition probabilities, the graph is gradually decreasing after forty-five (45) months. The result show that φ₁₁ (n), φ₂₂ (n), φ₃₃ (n) and φ₄₄ (n)attained the values of about 0.56516, 0.50353, 0.53343 and 0.65623 respectively for the first few months or years. The percentage decrease is about 37.1%, 17.8% for stages 2, 3 in forty-four months and 5.8% for stage 4 in forty-five month duration. However, client’s transitions dropped slowly and attain stability of stage at infinity. In compliance to the medical view, all HIV-naïve patients transit to AIDs stage especially when therapeutic intervention is lacking. The model established in this study could assist the Medical Personnels’ (MP), Health Care Providers (HCP), Epidemiologists, Medical Statisticians and other funding organizations to plan for the treatment, tracking and intervention for the ever increasing scourge of HIV/AIDs.