Optimal Control Applied to the Spread of Buruli Uclcer Disease

Optimal control theory is applied to a system of ordinary differential equations modeling Buruli ulcer transmission in population. We apply controls on mass treatment, insecticide and mass education to minimize the number of infected hosts and infected vectors as well as infected fishes. The model takes into account human, water bug and fish populations as well as MU in the environment. The host, vector and small fish are all assumed constant. First, we investigated the existence and stability of equilibria of the model without control based on the basic reproduction ratio. We then, applied Pontryagins maximum principle to characterize the optimal control. The optimality system is determined and computed numerically for several scenarios.