Optimal control analysis of HIV/AIDS and COVID-19 co-infection model with liver toxicity

Abstract

Co-infection with HIV/AIDS and COVID-19 presents a significant global health challenge, especially due to its association with liver toxicity a critical complication exacerbated by antiretroviral and antiviral therapies. Despite extensive modeling of HIV/AIDS or COVID-19 independently, few studies address the interplay of co-infection with liver toxicity. This study fills that gap by developing a novel compartmental model that captures the dynamics of HIV/AIDS and COVID-19 co-infection with acute and chronic liver toxicity, incorporating seven time-dependent optimal control strategies that represent both preventive and therapeutic interventions. Unlike prior models, our work integrates liver toxicity as a distinct health outcome and evaluates the combined effects of educational and medical interventions using Pontryagin’s Maximum Principle. The model's sensitivity analysis reveals that transmission and treatment rates significantly influence disease dynamics. Numerical simulations demonstrate that the simultaneous implementation of all seven controls three prevention and four treatments measures is the most effective strategy for minimizing co-infection prevalence and liver toxicity burden. The study concludes that integrated, multi-faceted intervention strategies are critical for effectively reducing the health impacts of HIV/AIDS and COVID-19 co-infection with liver toxicity. These findings offer actionable insights for policymakers and health planners aiming to improve public health outcomes in settings burdened by both diseases.