Optimal Control for a Nonlinear Tuberculosis Model

A system of partial differential equations modeling the transmission dynamics of tuberculosis is considered to represent the density of susceptible, vaccinated, latent stage infected, active stage infected, and treated individuals.We studied the optimal control problem of the coupled nonlinear system with nonlocal diffusion. First, an optimal solution for the proposed model is established and we derive the optimality system. Then, solutions for the direct and the adjoint problem are proved. Numerical simulations are provided to validate the theoretical results.