A Stochastic Model for Assessing the Efficacy of Antiretroviral Therapy (ART) on Farmers Living with HIV/AIDS

Abstract

The Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS) remains one of the greatest public health challenges still facing Nigeria and the entire world as it has become drug resistant in some patients. Hence, treatment failure and spread of drug resistant HIV/AIDS results. In view of this, it becomes imperative to assess the efficacy of the Antiretroviral Therapy (ART) treatment and hence the life expectancy of the HIV/AIDS patients. This was achieved in this study via a stochastic model based on the Markov chain modelling methodology. The CD4 cell counts of a sample of 28,582 patients (farmers) receiving treatment every six (6) months at the HIV counselling and Testing (HCT) unit of the Federal Medical Centre Makurdi, Benue State was used in the modelling process. The CD4 cell count states were developed based on the United States Centres for Disease Control and Prevention (CDC) classification system as follows; State 1: CD4 cell counts ≥ 500 cells/μL, State 2: CD4 cell count in the range of 200 – 499 cells/ μL, and State 3: CD4 cell count < 200 cells/ μL. They represent the Good, Moderate and Poor health states of the patients respectively. The HIV/AIDS progression in the study was investigated using The N-Step transition probability Matrix of the Markov Chain while, the efficacy of the ART was examined from one CD4 cell count state to another using the Steady State probabilities of the Markov Chain as well as the Mean Recurrence Time of each CD4 count state. The study result shows that; the initial probabilities that a patient will stay in the good, moderate, and poor health states in the first six (6) months of the ART are; 0.834, 0.333 and 0.280 respectively. The overall efficacy of the ART showed a 78%, 19%, and 3.3% chances that a patient will be in the Good, Moderate and Poor health states respectively with respective mean recurrence times of 0.64, 2.69 and 14.99 years. Further results shows that the total life expectancy of patients in the good and moderate health states are 20.425 and 19.275 years respectively. The study recommends that the methodology be applied to a cohort study to further validate study these results.