A fractional model is developed to study the transmission dynamics of tu- berculosis disease. The use of a fractional model provides a memory effect and long-term dynamics often observed in chronic infectious diseases such as tuberculosis, which is charac- terized by a prolonged incubation period and risks of reactivation. The basic reproduction number is computed and we derive the qualitative stability analysis of equilibria. A sensi- tivity analysis is conducted to assess the impact of the model parameters. Three control strategies are applied, namely treatment, vaccination, and infection rate management, to minimize the number of infected individuals. Numerical simulations are carried out to illustrate the theoretical results obtained.

fractional order; optimal control; tuberculosis; sensitivity analysis