Numerical and Theoretical Treatments of the Optimal Control Model for the Interaction Between Diabetes and Tuberculosis

We primarily focus on the formulation, theoretical, and numerical analyses of a non-autonomous model for tuberculosis (TB) prevention and control programs in a population where individuals suffering from the double trouble of tuberculosis and diabetes are present. The model incorporates four time-dependent control functions, saturated treatment of non-infectious individuals harboring tuberculosis, and saturated incidence rate. Furthermore, the basic reproduction number of the autonomous form of the proposed optimal control mathematical model is calculated. Sensitivity indexes regarding the constant control parameters reveal that the proposed control and preventive measures will reduce the tuberculosis burden in the population. This study establishes that the combination of campaigns that teach people how the development of tuberculosis and diabetes can be prevented, a treatment strategy that provides saturated treatment to non-infectious individuals exposed to tuberculosis infections, and prompt effective treatment of individuals infected with tuberculosis disease is the optimal strategy to achieve zero TB by 2035.