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Dynamic analysis and optimal control of a fractional order model for hand-foot-mouth Disease

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Abstract

In this paper, a fractional order mathematical model is constructed to describe the transmission of hand-foot-mouth disease. Two cases are considered: constant control and optimal control. In the former case, the existence and uniqueness of positive solutions are proved; then the sufficient conditions for the existence and stability of two equilibriums are obtained. In the latter case, the existence of an optimal control solution is obtained; next, the optimality control conditions are derived by using Pontryagin’s Maximum Principle. After that, some numerical simulations are performed to verify the theoretical prediction.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments, which improved the quality of this paper greatly.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Shanxi Normal University, Linfen, 041004, China

    Ruiqing Shi & Ting Lu

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  1. Ruiqing Shi
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  2. Ting Lu
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Each of the authors, RS, TL contributed to each part of this work equally and read and approved the final version of the manuscript.

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Correspondence to Ruiqing Shi.

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Shi, R., Lu, T. Dynamic analysis and optimal control of a fractional order model for hand-foot-mouth Disease. J. Appl. Math. Comput. 64, 565–590 (2020). https://doi.org/10.1007/s12190-020-01369-w

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