Mathematical Analysis of HIV/AIDS Anti-Retroviral Treatment Incorporating Adherence

Abstract

Current treatment for HIV infection consists of Highly Active Antiretroviral (ART) therapy. However, lack of adherence to ART treatment has hampered the bene ts of the ART treatment strategy and viral load suppression. Most of the treatment models studied so far do not explicitly include the relationship between adherence to ART regimens and viral load suppression. In this study, a mathematical model with ART adherence is developed. By an application of the next generation matrix approach, the reproduction number, R0, is determined.Stability analysis of the model developed shows that the Disease Free Equilibrium (DFE) is locally asymptotically stable, if R0 < 1; and an Endemic Equilibrium (EE) exists, which is unique and is locally asymptotically stable when R0 > 1. Using Lyapunov functional approach, the endemic equilibrium is shown to be globally asymptotically stable, and hence persistence of the disease in the population. Sensitivity analysis of the model shows that the disease can be kept under check if the test and treat strategy is upscaled as well as adherence to treatment for the infected individuals is emphasized.