Asian Journal of Pure and Applied Mathematics

The study extends the HIV/AIDS model, investigating the existence and Optimal control of the Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS).  HIV is a viral infection that attacks the body’s immune system, while AIDS is the most advanced stage of HIV infection, characterized by a severely immune system. This study formulates a deterministic mathematical model incorporating three time-dependent optimal control strategies. A comparative analysis of three control strategies was incorporated namely : awareness campaigns, treatment with ART, and targeted outreach programs. Using Pontryagins Maximum principle, we characterize the optimal control strategies and prove the existence of solutions. Numerical simulations using Matlab software illustrate the effectiveness of the proposed control strategies, highlighting the importance of tailored interventions and sustained investment in HIV/AIDS control programs. The study provides valuable insights into HIV/AIDS dynamics and optimal control strategies, emphasizing the need for context-specific interventions and sustained investment in HIV/AIDS control programs. The results show that combined implementation of awareness campaigns, treatment with ART, and targeted outreach significantly reduces AIDS cases and suppress AIDS-related outcomes, while treatment and targeted outreach effectively manage the disease. Our results provide valuable insights into effective control strategies and inform public health policies for HIV preventive and control. The findings indicate that the combined implementation of all strategies yields the most significant reduction in reducing the spread of HIV.