EXISTENCE AND OPTIMAL CONTROL ANALYSIS OF HIV/AIDS MODEL

Human Immunodeficiency Virus/ Acquired Immune Deficiency Syndrome (HIV/AIDS) stands as a paramount global health concern, being both a prevalent sexually transmitted disease and one of the most catastrophic epidemics ever recorded, with profound impacts on human health. This study revisits the theme of Odebiyi et al. The study presents a mathematical model describing HIV/AIDS transmission dynamics, incorporating optimal control strategies for public sensitization and the use of antiretroviral treatment thereby providing new insight to their work. Analytical results via optimal control theory confirm the existence of optimal solutions. Numerical Simulation results illustrate the efficacy of public sensitization and treatment in controlling HIV/AIDS. The combined implementation of these control measures yields significant reductions in HIV transmission. The analysis underscores the importance of multi-faceted HIV control strategies. Our findings are expected to inform policymakers in developing targeted interventions, optimizing resource allocation, and enhancing the impact of HIV control programs.