  We propose and analyse an optimal control problem where the control system is
a mathematical model for tuberculosis that considers reinfection. The control
functions represent the fraction of early latent and persistent latent
individuals that are treated. Our aim is to study how these control measures
should be implemented, for a certain time period, in order to reduce the number
of active infected individuals, while minimizing the interventions
implementation costs. The optimal intervention is compared along different
epidemiological scenarios, by varying the transmission coefficient. The impact
of variation of the risk of reinfection, as a result of acquired immunity to a
previous infection for treated individuals on the optimal controls and
associated solutions, is analysed. A cost-effectiveness analysis is done, to
compare the application of each one of the control measures, separately or in
combination.
