Optimal control for a tuberculosis model with reinfection and post-exposure interventions

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions, considering reinfection and post-exposure interventions. They depend on the parameters of the model and reduce effectively the number of active infectious and persistent latent individuals. The time that the optimal controls are at the upper bound increase with the transmission coefficient. A general explicit expression for the basic reproduction number is obtained and its sensitivity with respect to the model parameters is discussed. Numerical results show the usefulness of the optimization strategies.