Modelling HIV/AIDS Infection Dynamics in the Presence of Interfered Interventions
Hillary Kiprop Kosgei *
Department of Mathematics and Actuarial Science, Kabarak University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Mathematical models are invaluable tools for describing and understanding disease dynamics. In this study, we propose and analyse a mathematical model for HIV/AIDS in order to assess the impact of interfered interventions on the disease dynamics. The model enables us to
study the role of treatment in the presence of interfered interventions, as a control strategy for reducing the HIV pandemic. We performed thorough qualitative analysis on the reproduction number of the model, R0. The global and local dynamics of the system are also considered,
that is, we analyse the two equilibria states of the model,namely; the disease-free equilibrium and a unique disease-persistent equilibrium. The disease-free steady state is shown to be globally asymptotically stable whenever R0 < 1 and the endemic equilibrium is globally asymptotically stable whenever R0 > 1. We conducted numerical simulations to support the analytical results. The results of the model analysis indicate that interference has the effect of reducing treatment uptake and increasing the rate of drop-outs. The results have implications in the designing of policies in countries with war, economic turmoil or any other form of disturbance.
Keywords: HIV/AIDS, interference;, reproduction number, treatment, mathematical model.