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

Author

Listed:
  • 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
    Department of Natural Sciences, College of Science and Technical Education, Mbeya University of Science and Technology, P.O. Box 131 Mbeya, 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)

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.

Suggested Citation

  • Mlyashimbi Helikumi & Moatlhodi Kgosimore & Dmitry Kuznetsov & Steady Mushayabasa, 2019. "Backward Bifurcation and Optimal Control Analysis of a Trypanosoma brucei rhodesiense Model," Mathematics, MDPI, vol. 7(10), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:971-:d:276335
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