A Deterministic Model of ART on HIV Spread Outcomes: A Case Study in Tanzania

Abstract

This is about understanding in a mathematical perspective, how the introduction of antiretroviral therapy (ART) is shaping the spread of HIV. A non-linear mathematical model for HIV transmission in a variable size population is formulated in this paper. The model is about analysis and simulation of HIV spread along with treating infected individuals with ARV therapy. Thus, the model is constructed by including individuals who are under ARV therapy as transmitters of HIV. This paper includes studying the speed of spread and how best could be controlled by including the concept of doubling time. The model’s point of equilibria have been found and their stability have been investigated. The model has two points of equilibria, the disease free and the endemic equilibrium. It has been found that if basic reproduction number, R0 < 1 the disease free equilibrium is asymptotically stable under some conditions. On the other hand if R0 > 1 the disease free equilibrium is not stable. In addition, when R0 > 1 there exist a unique endemic equilibrium, which is found to be both locally and globally stable under some conditions.Simulations of the model have been conducted, taking Tanzania as a case study for the year 2015 onwards. Initial values for the population size start in 2015, and the endemic equilibrium has been estimated. The measures to control the spread of HIV have been suggested to ensure that R0 < 1. One of the case simulated is that R0 = 0.6875 < 1, in which the epidemic diminishes. When R0 > 1 the disease grows, and this has been simulated for R0 = 1.3 > 1.