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Research Article | Open Access

Modeling and analysis of fractional order Zika model

Muhammad Farman1Ali Akgül2Sameh Askar3Thongchai Botmart4( )Aqeel Ahmad1Hijaz Ahmad5
Department of Mathematics and Statistics, University of Lahore, Lahore 54590, Pakistan
Art and Science Faculty, Department of Mathematics, Siirt University, Siirt 56100, Turkey
Department of Statistics and Operations Research, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
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Abstract

We propose mathematical model for the transmission of the Zika virus for humans spread by mosquitoes. We construct a scheme for the Zika virus model with Atangna-Baleanue Caputo sense and fractal fractional operator by using generalized Mittag-Leffler kernel. The positivity and boundedness of the model are also calculated. The existence of uniquene solution is derived and stability analysis has been made for the model by using the fixed point theory. Numerical simulations are made by using the Atangana-Toufik scheme and fractal fractional operator with a different dimension of fractional values which support the theoretical outcome of the proposed system. Developed scheme including simulation will provide better understanding in future analysis and for control strategy regarding Zika virus.

CLC number: 37C75, 93B05, 65L07

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AIMS Mathematics
Pages 3912-3938

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Cite this article:
Farman M, Akgül A, Askar S, et al. Modeling and analysis of fractional order Zika model. AIMS Mathematics, 2022, 7(3): 3912-3938. https://doi.org/10.3934/math.2022216

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Received: 26 September 2021
Accepted: 10 November 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)