MATHEMATICAL MODELING OF HIV TRANSMISSION DYNAMICS WITH ANTIRETROVIRAL THERAPY, TREATMENT ADHERENCE, AND TIME DELAY: STABILITY AND NUMERICAL ANALYSIS

Abstract

This study presents a mathematical model to analyse the transmission dynamics of Human Immunodeficiency Virus (HIV) by incorporating antiretroviral therapy (ART), treatment adherence, and delay in treatment initiation. The model divides the population into susceptible, infected, and treated compartments, allowing a realistic representation of disease progression. A system of nonlinear differential equations with time delay is formulated and analyzed to determine equilibrium points and the basic reproduction number. The stability of the disease-free equilibrium is examined, showing that the infection dies out when the reproduction number is less than unity, while persistence occurs otherwise. Numerical simulations are performed to investigate the impact of key parameters on disease dynamics. The results demonstrate that ART significantly reduces infection levels; however, its effectiveness strongly depends on treatment adherence and timely initiation. Higher adherence leads to a rapid decline in infected individuals, whereas delays in treatment contribute to sustained transmission. The findings also highlight the importance of reducing transmission rates through preventive measures. The study provides valuable insights for designing effective intervention strategies and supports global efforts aligned with the Sustainable Development Goal 3 (Good Health and Well-being), particularly Target 3.3, which aims to end the HIV/AIDS epidemic by 2030.