Analysis of HIV/AIDS and HBV co-infection with drug-induced hepatotoxicity compartmental model with optimal control theory.

HIV/AIDS and Hepatitis B virus (HBV) co-infection poses a major public health threat, often complicated by drug-induced hepatotoxicity from antiretroviral therapy, a critical aspect overlooked in previous mathematical models. This study develops and analyzes a novel 12-compartment model to understand the co-dynamics of these diseases and treatment-related liver damage. We determined the model's equilibrium points and basic reproduction number and applied Optimal Control Theory to evaluate seven time-dependent interventions, including protection measures and treatments. Numerical simulations identified a combined strategy (Strategy 12) simultaneously implementing protection against HIV, HBV, and co-infection alongside targeted treatment for co-infected individuals and those with drug-induced hepatotoxicity as the most effective approach. The findings underscore the necessity of integrated public health strategies that address infection prevention, treatment, and the management of adverse drug effects to alleviate the disease burden.