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

•We investigate a tuberculosis model from the optimal control point of view.•Optimal policies are proposed to minimize the cost of interventions.•Optimal controls reduce both active infectious and persistent latent individuals.•Optimal control strategies consider reinfection and post-exposure interventions.•The time controls are at the upper bound, increase with the transmission coefficient.

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.