Optimal control of Human African Trypanosomiasis in a population with endemic malaria

Optimal control theory is applied to a system of ordinary differential equations modelling a co-infection of malaria and sleeping sickness. The objective is to minimise chances of a malaria individual acquiring sleeping sickness. Two controls are used, one preventing infection and another preventing bites by the tsetse fly to the co-infected. The optimal controls are characterized in terms of the optimality system, which is solved numerically for three different scenarios. Results show that controlling co-infections of malaria and sleeping sickness can best be achieved if the bites from the tsetse fly are prevented.