Dynamical and optimal control analysis of a seasonal <em>Trypanosoma brucei rhodesiense</em> model

Mlyashimbi Helikumi; Moatlhodi Kgosimore; Dmitry Kuznetsov; Steady Mushayabasa; Mlyashimbi Helikumi; Moatlhodi Kgosimore; Dmitry Kuznetsov; Steady Mushayabasa

doi:10.3934/mbe.2020139

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 3: 2530-2556. doi: 10.3934/mbe.2020139

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Research article

Dynamical and optimal control analysis of a seasonal Trypanosoma brucei rhodesiense model

1.
Institution of Science and Technology (NM-AIST), School of Computational and Communication Science and Engineering, The Nelson Mandela African, P. O. Box 447, Arusha, Tanzania
2.
Department of Mathematics and Statistics, Mbeya University of Science and Technology, College of Science and Technical Education, P. O. Box 131, Mbeya, Tanzania
3.
Department of Basic Sciences, Botswana University of Agriculture and Natural Resources Private Bag 0027, Gaborone, Botswana
4.
Department of Mathematics, University of Zimbabwe, P. O. Box MP 167, Harare, Zimbabwe

Received: 14 November 2019 Accepted: 07 February 2020 Published: 27 February 2020

The effects of seasonal variations on the epidemiology of Trypanosoma brucei rhodesiense disease is well documented. In particular, seasonal variations alter vector development rates and behaviour, thereby influencing the transmission dynamics of the disease. In this paper, a mathematical model for Trypanosoma brucei rhodesiense disease that incorporates seasonal effects is presented. Owing to the importance of understanding the effective ways of managing the spread of the disease, the impact of time dependent intervention strategies has been investigated. Two controls representing human awareness campaigns and insecticides use have been incorporated into the model. The main goal of introducing these controls is to minimize the number of infected host population at low implementation costs. Although insecticides usage is associated with adverse effects to the environment, in this study we have observed that by totally neglecting insecticide use, effective disease management may present a formidable challenge. However, if human awareness is combined with low insecticide usage then the disease can be effectively managed.
- Trypanosoma brucei rhodesiense,
- seasonality,
- stability,
- optimal control
Citation: Mlyashimbi Helikumi, Moatlhodi Kgosimore, Dmitry Kuznetsov, Steady Mushayabasa. Dynamical and optimal control analysis of a seasonal Trypanosoma brucei rhodesiense model[J]. Mathematical Biosciences and Engineering, 2020, 17(3): 2530-2556. doi: 10.3934/mbe.2020139

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Abstract

The effects of seasonal variations on the epidemiology of Trypanosoma brucei rhodesiense disease is well documented. In particular, seasonal variations alter vector development rates and behaviour, thereby influencing the transmission dynamics of the disease. In this paper, a mathematical model for Trypanosoma brucei rhodesiense disease that incorporates seasonal effects is presented. Owing to the importance of understanding the effective ways of managing the spread of the disease, the impact of time dependent intervention strategies has been investigated. Two controls representing human awareness campaigns and insecticides use have been incorporated into the model. The main goal of introducing these controls is to minimize the number of infected host population at low implementation costs. Although insecticides usage is associated with adverse effects to the environment, in this study we have observed that by totally neglecting insecticide use, effective disease management may present a formidable challenge. However, if human awareness is combined with low insecticide usage then the disease can be effectively managed.

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