Optimal Control Analysis of HIV/AIDS Model with PrEP Strategy and Behavioral Changes

Combining Pre-Exposure Prophylaxis (PrEP) with behavioral strategies has become vital in curbing HIV/AIDS transmission, offering a pathway to reduce infections and allocate health resources more effectively. In this study, we developed a six-compartment mathematical model to analyze the spread and control of HIV/AIDS. Through rigorous analysis, we calculated the basic reproduction number (R₀) to assess transmission potential and evaluated the stability of the disease-free equilibrium state. To identify optimal strategies for reducing HIV/AIDS prevalence, we designed an optimal control framework using Pontryagin’s Minimum Principle. This approach allowed us to evaluate the effectiveness of prevention tactics such as public health education, condom use, screening, and treatment both individually and in combination. Our findings highlight that pairing community awareness campaigns with increased condom usage among adults, alongside proactive screening and treatment programs, significantly reduces new infections and overall prevalence. Numerical simulations further demonstrated how these measures lower infection rates, aligning with our theoretical predictions. These insights emphasize the importance of integrated, multi-pronged interventions to guide public health policies and resource distribution in the fight against HIV/AIDS.