Modeling the Dynamics of Tuberculosis-Diabetes Mellitus Coinfection with an Optimal Control Approach

Tuberculosis–Diabetes Mellitus (TB-DM) coinfection poses a significant public health challenge, contributing to increased morbidity, treatment failure, and healthcare costs. This study develops a mathematical model that stratifies TB infection into latent and active classes to examine the dynamics of TB–DM coinfection. The model is analyzed to determine the disease-free and endemic equilibrium points, supported by numerical evaluation using established parameter values. Furthermore, prevention strategies are assessed through an optimal control framework, formulated using Pontryagin’s Minimum Principle and validated through numerical simulations. The findings are expected to provide effective strategies to reduce TB-DM transmission and minimize optimal control costs, thereby supporting the development of improved public health policies.