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Stability analysis and optimal control of a fractional human African trypanosomiasis model

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  • Bonyah, Ebenezer
  • Gómez-Aguilar, J.F.
  • Adu, Augustina

Abstract

Human African trypanosomiasis has been a major problem in sub-Saharan countries including Ghana. In this paper, a fractional human African trypanosomiasis model with fractional time dependent control is studied. The existence and uniqueness of the model were obtained. Collected data from Ghana were considered to fit the derived model. Fractional optimal control via Atangana–Baleanu derivative in Liouville–Caputo sense is used to determine the best strategy for minimizing the spread of human African trypanosomiasis. The numerical result shows that the combination of three controls is effective, however the combination of prevention and treatment can also offer a good strategy since the cost for implementing two controls is lower than three controls.

Suggested Citation

  • Bonyah, Ebenezer & Gómez-Aguilar, J.F. & Adu, Augustina, 2018. "Stability analysis and optimal control of a fractional human African trypanosomiasis model," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 150-160.
    • Handle: RePEc:eee:chsofr:v:117:y:2018:i:c:p:150-160
    DOI: 10.1016/j.chaos.2018.10.025
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    References listed on IDEAS

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    1. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    2. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
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    Cited by:

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    6. Pho, Kim-Hung & Heydari, M.H. & Tuan, Bui Anh & Mahmoudi, Mohammad Reza, 2020. "Numerical study of nonlinear 2D optimal control problems with multi-term variable-order fractional derivatives in the Atangana-Baleanu-Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).

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