Optimal Control of Tuberculosis: A Review

We review the optimal control of systems modeling the dynamics of tuberculosis. Time dependent control functions are introduced in the mathematical models, representing strategies for the improvement of the treatment and cure of active infectious and/or latent individuals. Optimal control theory allows then to find the optimal way to implement the strategies, minimizing the number of infectious and/or latent individuals and keeping the cost of implementation as low as possible. An optimal control problem is proposed and solved, illustrating the procedure. Simulations show an effective reduction in the number of infectious individuals.