title: Optimal control for a tuberculosis model with reinfection and post-exposure interventions.
abstract: 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.
authors.affiliation: CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal. cjoaosilva@ua.pt
authors.forename: Cristiana J
authors.initials: CJ
authors.lastname: Silva
authors.forename: Delfim F M
authors.initials: DF
authors.lastname: Torres
mesh_terms: D058872:Epidemics / Q000191:economics / Q000517:prevention & control; D006801:Humans; D007837:Latency Period, Psychological; D008954:Models, Biological; D055502:Secondary Prevention; D014376:Tuberculosis / Q000191:economics / Q000453:epidemiology* / Q000517:prevention & control; D032581:Tuberculosis Vaccines / Q000191:economics / Q000627:therapeutic use
chemical_list: D032581:Tuberculosis Vaccines
keywords: Epidemic model; Optimal control theory; Treatment strategies; Tuberculosis