A mathematical and sensitivity analysis of an HIV/AIDS infection model

Abstract

Over the past decade, Human Immunodeficiency Virus infection and Acquired Immunodeficiency Syndrome (HIV/AIDS) have become deadly infectious diseases, particularly in developing countries. This challenge has led to the development of some important HIV/AIDS treatment strategies, such as antiretroviral therapy (ART), among many others. This study presents a mathematical model to investigate the dynamics of HIV/AIDS transmission. Employing mathematical analysis, non-negativity, boundedness, the basic reproduction number ℛ 0, and the stability of both the disease-free and endemic equilibrium of the proposed model were derived. Normalized forward sensitivity techniques are used to determine the significance and importance of sensitive parameters associated with ℛ 0. To gain insights into the dynamical behavior of each compartment, an effective numerical scheme was utilized, and the results obtained suggest that there is a need, even if individuals are infected with the virus, to use non-pharmaceutical interventions as control strategies.