Pseudospectral Method based Optimal Control of Tuberculosis Model

This paper discusses the use of optimal control strategies for ascertaining efficient usage of infection eliminating methodologies. The mathematical model of tuberculosis is considered which is incorporated with three control terms. The preventive controls used for containing the spread of tuberculosis, include vaccinations along with treatment control for the latent, susceptible and infected population. By implementing Pseudospectral method on the Tuberculosis model, the original continuous time optimal control problem is converted into its equivalent non-linear programming problem and then solved. On application of the proposed control scheme, a minimization in the intervention cost and a significant reduction in the disease burden is expected. A comparative analysis between the widely used Legendre Pseudospectral method and Chebyshev Pseudospectral method when applied to the mathematical model of tuberculosis is included in this work. The response of the states in absence of any control effort is also included to demonstrate the effect of optimal control strategy on the disease.