Mathematical Modeling and Optimal Control Strategies of HIV/AIDS with HAART

Abstract

The human immunodeficiency virus (HIV) and acquired immune deficiency syndrome (AIDS) have posed one of the most pressing problems for world health and development, ever since its discovery in the early 1980s. The spread of Human immunodeficiency virus (HIV) is a worldwide health concern. According to the WHO's estimate of the global HIV epidemic in 2021, 650 000 [510 000–850 000] individuals worldwide died in 2021 as a result of HIV-related causes. In this study, we proposed a mathematical model to study the effects of counselling and screening of unaware infective on the transmission dynamics of HIV/AIDS in the presence of highly active antiretroviral therapy (HAART). We investigate the optimal amounts of various intervention measures required to decrease disease transmission and boost output. To do this, we alter our basic model to include various intervention techniques in order to obtain an optimal control problem, which is then qualitatively assessed using Pontryagin's Maximum principle. To obtain greater insight into the ramifications of the interventions, the resulting optimal control problem is numerically analysed using an iterative method – forward-backwards sweep Runge-Kutta fourth-orderr numerical approximation methodology. Then, using time as a control, we design the optimal control problems and devise a strategy to lower the number of infected people and the associated costs. Finally, numerical simulation findings reveal that the most efficient strategy to limit HIV infection is to use the optimal combination of condoms on susceptible and on infection transmission rate, counselling and testing on unaware infective, and treatment on aware HIV/AIDS infectives.