Tuberculosis is caused by Mycobacterium tuberculosis. The disease is still one of the major killer of humans. We derive and analyzed mathematical modeling of drug resistance in tuberculosis transmission. We use control on treatment to reduce of the number of infected population. For model without control optimal, we have the basic reproduction number for the sensitive and resistant tuberculosis infection in the first area and tuberculosis infection in the second area. This number determine the existence and stability of equilibria. Then, the Pontryagin Maximum Principle is applied to derive necessary conditions for the optimal control of the tuberculosis disease. Finally, numerical simulations are performed to describe the analytical results.
- Mathematical model
- Optimal control