A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative

We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We pr...

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Detalles Bibliográficos
Autores principales: Baleanu, Dumitru, Mohammadi, Hakimeh, Rezapour, Shahram
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2020
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7301114/
https://www.ncbi.nlm.nih.gov/pubmed/32572336
http://dx.doi.org/10.1186/s13662-020-02762-2
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author Baleanu, Dumitru
Mohammadi, Hakimeh
Rezapour, Shahram
author_facet Baleanu, Dumitru
Mohammadi, Hakimeh
Rezapour, Shahram
author_sort Baleanu, Dumitru
collection PubMed
description We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.
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spelling pubmed-73011142020-06-18 A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative Baleanu, Dumitru Mohammadi, Hakimeh Rezapour, Shahram Adv Differ Equ Research We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative. Springer International Publishing 2020-06-18 2020 /pmc/articles/PMC7301114/ /pubmed/32572336 http://dx.doi.org/10.1186/s13662-020-02762-2 Text en © The Author(s) 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Research
Baleanu, Dumitru
Mohammadi, Hakimeh
Rezapour, Shahram
A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title_full A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title_fullStr A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title_full_unstemmed A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title_short A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative
title_sort fractional differential equation model for the covid-19 transmission by using the caputo–fabrizio derivative
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7301114/
https://www.ncbi.nlm.nih.gov/pubmed/32572336
http://dx.doi.org/10.1186/s13662-020-02762-2
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