<![CDATA[Tuberculosis–Diabetes Mellitus (TB–DM) coinfection increases morbidity, treatment failure, and healthcare costs. This study analyzes TB–DM transmission dynamics and identifies effective prevention strategies using a ten-compartment mathematical model that distinguishes non-diabetic and diabetic populations, each classified into susceptible, latent, active, treatment, and recovered classes. Numerical analysis verifies that the disease-free equilibrium is stable when the basic reproduction number is less than one, whereas an endemic equilibrium exists when it exceeds one. Using baseline parameter values, the reproduction number is estimated as 3.592, indicating persistent TB–DM transmission. An optimal control framework is formulated to evaluate two time-dependent interventions: reducing TB transmission through case detection and contact tracing, and preventing diabetes onset in non-diabetic individuals through metabolic monitoring. Numerical simulations demonstrate that the combined implementation of both control strategies significantly reduces TB–DM incidence while minimizing intervention costs. These findings support the importance of integrated, time-varying TB–DM control programs for public health.]]>
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