Analysis of a Mathematical Model Incorporating Dual Protection and ART Adherence for a High Risk HIV Population

Abstract

In this paper, a mathematical model for dual protection, incorporating PrEP and Condom use, and ART adherence is formulated, based on a system of ordinary differential equations and analyzed. The results obtained from stability analysis indicate that provided the basic reproductive number is less than unity, the disease free equilibrium point is both locally and globally asymptotically stable, while provided the basic reproductive number is greater than unity, the endemic equilibrium point exists and is locally asymptotically stable. Sensitivity analysis is undertaken to establish the most sensitive model parameter. The most sensitive parameter to the value of R₀ is β₁, the mean contact rate with undiagnosed infectives. This implies that in order to control the spread of HIV in a high risk population, efforts should be geared towards reducing the undiagnosed by testing and enrolling them on ART treatment. This in turn lowers their infectivity as well as chances of progressing to the AIDS class.