A Mathematical Model for the Prevention of HIV/AIDS in the Presence of Undetectable Equals Untransmittable Viral Load

Abstract

Recent advancement in medicine has brought about the use of Antiretroviral Therapy (ART) treatment regime to reduce the viral load of a Human Immunodeficiency Virus (HIV) or Acquired Immune Deficiency Syndrome (AIDS) patients to an Undetectable equals Untransmittable (U=U) level. While half of HIV-positive individuals in the United States have achieved an undetectable viral load, African countries face distinct challenges, including unawareness of the possibility of attaining the U=U viral load. This paper presents a novel mathematical model for HIV/AIDS transmission in Africa, using Cape Verde as a case study, by incorporating the ART treatment, resulting in U=U. The qualitative properties of the model, including the boundedness and positivity of its solution were obtained. Local and global stability analyses of the Disease-Free Equilibrium (DFE) point of the model were performed using the next generation matrix approach and the direct Lyapunov method respectively. The result indicated that the DFE of the model is stable and the disease cannot invade the studied population. The model equations were solved through the implementation of MATLAB ODE45 algorithm and simulations were performed to visualize the effects of the ART on attaining a U=U viral load.