Optimal Control Analysis of Transmission Dynamics and Treatment Pathways in a TB–HCV Co-Infection Model

Abstract

This study develops a deterministic compartmental model to investigate the effects of partial treatment on the transmission dynamics of tuberculosis (TB) and hepatitis C virus (HCV) co-infection and to identify effective intervention strategies. The basic reproduction number was derived using the next-generation matrix method, and sensitivity analysis was conducted to determine the parameters most influential in disease transmission. The results show that transmission-related parameters have the greatest influence on the reproduction number, while treatment-related parameters substantially reduce the burden of TB–HCV co-infection. Numerical simulations further indicate that partial treatment prolongs infectiousness, accelerates disease progression, and enhances interactions between TB and HCV, with TB identified as the dominant contributor to co-infection dynamics. An optimal control model incorporating awareness, detection, and treatment interventions was formulated using Pontryagin's Maximum Principle. Numerical simulations demonstrate that the simultaneous implementation of these interventions can substantially reduce TB–HCV co-infection, with near elimination achievable within two years. Based on these findings, individuals diagnosed with either TB or HCV should be routinely screened for the other infection to facilitate early detection and timely concurrent treatment.