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Optimal Control Applied to a Fractional-Order Foot-and-Mouth Disease Model

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Abstract

In this paper, we propose a nonlinear fractional-order model in order to explain and understand the outbreaks of foot-and-mouth disease. The proposed model rely on the Caputo operator. We computed the basic reproduction number and demonstrated that it is an important metric for extinction and persistence of the disease. Utilizing reported foot-and-mouth disease data for Zimbabwe and the nonlinear least-squares curve fitting method we estimated the model parameters. Meanwhile, we performed an optimal control study on the use of animal vaccination and culling of infectious animals as disease control measures against foot-and-mouth disease. Our findings showed combinations of optimal vaccination and culling rates that could lead to the effective management of the disease.

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Data Availibility Statement

The data used to support the findings of this study are included within the article.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, National University of Science and Technology, P. O. Box 939, Ascot, Bulawayo, Zimbabwe

    Tinashe B. Gashirai & Senelani D. Hove-Musekwa

  2. Department of Mathematics and Computational Sciences, University of Zimbabwe, P.O. Box MP 167, Harare, Zimbabwe

    Steady Mushayabasa

Authors
  1. Tinashe B. Gashirai
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  2. Senelani D. Hove-Musekwa
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  3. Steady Mushayabasa
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Contributions

Gashirai, B.T.: Conceptualization, Formal analysis and Methodology. Hove-Musekwa, S.D.: Original draft preparation. Mushayabasa, S.: Software, Validation, Writing-Reviewing and Editing.

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Correspondence to Steady Mushayabasa.

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Gashirai, T.B., Hove-Musekwa, S.D. & Mushayabasa, S. Optimal Control Applied to a Fractional-Order Foot-and-Mouth Disease Model. Int. J. Appl. Comput. Math 7, 73 (2021). https://doi.org/10.1007/s40819-021-01011-8

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