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In this current study, the theory of optimal control is applied to the model of tuberculosis with a multidrug-resistant compartment. It is assumed that latent case finding, case holding, and case management are the main controls for TB disease. The objective of optimal controls is to reduce the number of infections that result from contact with infectious individuals while minimizing the cost associated with control measures. To achieve this goal, Pontryagin’s maximum principle is applied and the existence of optimal controls is verified. Moreover, numerical simulations have been carried out using forward and backward sweeps in time based on fourth-order Runge–Kutta schemes. Simulation of the model, by considering different strategies, is carried out to examine which alternative might yield the most favorable results. The findings indicate that a strategy that combines all three controls (latent case finding, case holding, and case management) is more beneficial in eliminating tuberculosis than the other strategies. In addition to this, cost-effectiveness analysis is performed using the incremental cost-effectiveness ratio (ICER). The ICER findings demonstrate that a strategy that incorporates all three controls (latent case finding, case holding, and case management) is the most cost-effective of all other strategies considered in this study. |
