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

B. Nannyonga; L. S. Luboobi

B. Nannyonga Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda
L. S. Luboobi Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda

Keywords: Human African Trypanosomiasis, Malaria, Co-Infection.

Abstract

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 minimisechances of a malaria individual acquiring sleeping sickness. Two controls areused, one preventing infection and another preventing bites by the tsetse fly to theco-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 thebites from the tsetse fly are prevented.

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