Mathematical Modeling and Analysis of HIV/AIDS with Optimal Control
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The human immunodeficiency virus (HIV) remains a significant global health challenge, affecting millions of people worldwide. Despite advancements in antiretroviral therapy (ART), the disease continues to spread due to direct human-to-human transmission and potential environmental reservoirs. This study develops a mathematical model that incorporates both transmission pathways, along with the impact of ART and environmental contamination. The model stratifies the population into compartments, including susceptible individuals, those with HIV, individuals receiving treatment, and those in the AIDS stage, as well as an additional compartment for HIV-contaminated materials. Stability and bifurcation analyses reveal conditions under which the disease-free equilibrium remains stable or transitions to an endemic state. The study also explores optimal control strategies using Pontryagin’s Maximum Principle to identify effective intervention measures. Numerical simulations demonstrate the importance of ART distribution, behavioral interventions, and environmental decontamination in reducing disease prevalence. These findings provide valuable insights for policymakers and public health officials in designing evidence-based strategies for mitigating HIV transmission and improving health outcomes.