Mathematical Model Dynamics of Drug‐Resistant Tuberculosis and Its Optimal Control Analysis

This study presents a mathematical model to understand and control the spread of drug‐resistant tuberculosis (DR‐TB). A system of nonlinear ordinary differential equations is developed to represent the transmission dynamics, incorporating prevention and treatment strategies. Well‐posedness, positivity, and boundedness of solution of the model are explained. The basic reproduction number is derived, and stability analysis of fixed point reveals that the disease‐free equilibrium is globally asymptotically stable when R 0 < 1. Sensitivity analysis identifies transmission rate and treatment effectiveness as key parameters influencing basic reproduction number. To optimize disease management, the model incorporates control strategies using Pontryagin’s minimum principle, minimizing both infections and intervention costs. Numerical simulations compare double and combined interventions, demonstrating that simultaneous application of all controls significantly reduces DR‐TB prevalence. Furthermore, cost‐effectiveness analysis highlights prevention and treatment of multidrug‐resistant TB as the most impactful strategies, providing actionable insights for policymakers in resource‐limited settings.