Backward Bifurcation and Optimal Control Analysis of a Trypanosoma brucei rhodesiense Model

Mlyashimbi Helikumi, Moatlhodi Kgosimore, Dmitry Kuznetsov and Steady Mushayabasa
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Mlyashimbi Helikumi: School of Computational and Communication Science and Engineering, The Nelson Mandela African Institution of Science and Technology, P.O. Box 447 Arusha, Tanzania
Moatlhodi Kgosimore: Department of Basic Sciences, Botswana University of Agriculture and Natural Resources, Private Bag 0027, Gaborone, Botswana
Dmitry Kuznetsov: School of Computational and Communication Science and Engineering, The Nelson Mandela African Institution of Science and Technology, P.O. Box 447 Arusha, Tanzania
Steady Mushayabasa: Department of Mathematics, University of Zimbabwe, P.O. Box MP 167 Harare, Zimbabwe

Mathematics, 2019, vol. 7, issue 10, 1-16

Abstract: In this paper, a mathematical model for the transmission dynamics of Trypanosoma brucei rhodesiense that incorporates three species—namely, human, animal and vector—is formulated and analyzed. Two controls representing awareness campaigns and insecticide use are investigated in order to minimize the number of infected hosts in the population and the cost of implementation. Qualitative analysis of the model showed that it exhibited backward bifurcation generated by awareness campaigns. From the optimal control analysis we observed that optimal awareness and insecticide use could lead to effective control of the disease even when they were implemented at low intensities. In addition, it was noted that insecticide control had a greater impact on minimizing the spread of the disease compared to awareness campaigns.

Keywords: human African trypanosomiasis; mathematical model; awareness programs; insecticide use; optimal control theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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