Mathematical modeling of Dual protection and art Adherence for a high risk HIV Population

Abstract

The spread of HIV/AIDS remains a major concern to public health enthusiasts world over. In spite of interventions such as medical male circumcision, condom use, treatment using Antiretroviral Therapy (ART), as well as use of Pre-Exposure Prophylaxis, the number of new HIV/AIDS infections in Sub-Sahara Africa remains high. This may be attributed to factors such as PrEP failure and inconsistency in condom use especially among the high risk group. The e ectiveness of condoms depends on quality and proper use, while the success of ART largely depends on adherence. Mathematical models for these interventions exist in literature. However the challenges associated with the use of a single approach consequently necessitate the use of dual protection for better outcome against infection especially for the high risk population. In this study, a mathematical model for dual protection, incorporating PrEP and Condom use, and ART adherence is formulated, based on a system of ordinary di erential equations and analyzed. The results obtained from stability analysis indicate that provided the basic reproductive number (R0) is less than unity, the disease free equilibrium point is both locally and globally asymptotically stable, while provided that R0 is greater than unity, the endemic equilibrium point is locally asymptotically stable. Sensitivity analysis showed that the most sensitive parameter is 1, the mean contact rate with undiagnosed infectives. Numerical simulation results revealed that dual protection and ART adherence are key in the ght against the spread of HIV among the high risk population. These ndings will help in reducing the number of new HIV infections as well as lower the infectivity of those who are already infected.