Optimal Control for a COVID-19 and Tuberculosis Co-Infection Model with Asymptomatic COVID-19 Carriers

This study applies optimal control theory to a deterministic co-infection model of COVID-19 and tuberculosis (TB) with asymptomatic COVID-19 carriers, who are assumed to be less infectious. The optimal control strategy aims to minimize intervention costs and reduce infections by implementing five control measures, including prevention and vaccination of COVID-19, treatment of both symptomatic and asymptomatic COVID-19-infected individuals, treatment of COVID-19 and active TB co-infected individuals, and prevention of treatment failure in active TB cases. Pontryagin's minimum principle is used to characterize the necessary conditions for optimal control in reducing infections. Numerical results demonstrate the effectiveness of the optimal control strategy in suppressing diseases. The incremental cost-effectiveness ratio (ICER) for different combinations of control measures is evaluated, showing that the intervention strategy performs best when all control measures are used.