On the Analytical Solution of Fractional SIR Epidemic Model
This article presents the solution of the fractional SIR epidemic model using the Laplace residual power series method. We introduce the fractional SIR model in the sense of Caputo’s derivative; it is presented by three fractional differential equations, in which the third one depends on the first c...
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| Published in: | Applied Computational Intelligence and Soft Computing Vol. 2023; pp. 1 - 16 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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New York
Hindawi
02.02.2023
John Wiley & Sons, Inc Wiley |
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| ISSN: | 1687-9724, 1687-9732 |
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| Abstract | This article presents the solution of the fractional SIR epidemic model using the Laplace residual power series method. We introduce the fractional SIR model in the sense of Caputo’s derivative; it is presented by three fractional differential equations, in which the third one depends on the first coupled equations. The Laplace residual power series method (LRPSM) is implemented in this research to solve the proposed model, in which we present the solution in a form of convergent series expansion that converges rapidly to the exact one. We analyze the results and compare the obtained approximate solutions to those obtained from other methods. Figures and tables are illustrated to show the efficiency of the LRPSM in handling the proposed SIR model. |
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| AbstractList | This article presents the solution of the fractional SIR epidemic model using the Laplace residual power series method. We introduce the fractional SIR model in the sense of Caputo's derivative; it is presented by three fractional differential equations, in which the third one depends on the first coupled equations. The Laplace residual power series method (LRPSM) is implemented in this research to solve the proposed model, in which we present the solution in a form of convergent series expansion that converges rapidly to the exact one. We analyze the results and compare the obtained approximate solutions to those obtained from other methods. Figures and tables are illustrated to show the efficiency of the LRPSM in handling the proposed SIR model. |
| Audience | Academic |
| Author | Saadeh, Rania Qazza, Ahmad |
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| Cites_doi | 10.18576/amis/130202 10.1142/p614 10.1515/nleng-2021-0022 10.1016/j.cam.2014.01.002 10.1007/978-981-16-0626-7 10.3390/math10152581 10.3390/sym14010050 10.1108/03684920910991540 10.3934/math.2023088 10.1016/j.cnsns.2010.07.016 10.1016/j.chaos.2020.109787 10.1016/j.aej.2021.07.020 10.1615/critrevbiomedeng.v32.i2.10 10.1016/j.mbs.2022.108926 10.1007/978-1-4939-9828-9 10.3390/math10071089 10.1140/epjp/s13360-020-01061-9 10.1016/j.aej.2022.04.004 10.1038/nrg2098 10.1016/j.chaos.2020.109957 10.3390/fractalfract6090490 10.1016/j.amc.2009.05.051 10.3934/math.2023267 10.3390/sym14071323 10.1155/2022/6939045 10.1016/j.chaos.2022.112394 10.1016/j.aej.2022.07.022 10.1142/6799 |
| ContentType | Journal Article |
| Copyright | Copyright © 2023 Ahmad Qazza and Rania Saadeh. COPYRIGHT 2023 John Wiley & Sons, Inc. Copyright © 2023 Ahmad Qazza and Rania Saadeh. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| References | 22 F. Mainardi (7) 2010 I. Podlubny (6) 1999 26 R. M. Anderson May (2) 1992 27 28 29 F. A. Rihan (17) 2021 30 31 G. P. Wormser (1) 2008 W. O. Kermack (3) 1927; 115 10 32 33 12 34 R. M. Merrill (4) 2019 13 35 14 Z. Ma (25) 2009 15 18 19 F. Brauer (24) 2019 5 A. A. Kilbas (11) 2006 8 9 N. I. Akinwande (23) 2013; 14 S. T. Vittadello (16) 2022; 354 20 21 |
| References_xml | – ident: 20 doi: 10.18576/amis/130202 – volume-title: Fractional Calculus and Waves in Linear Viscoelasticity year: 2010 ident: 7 doi: 10.1142/p614 – volume-title: Theory and Applications of Fractional Differential Equation year: 2006 ident: 11 – ident: 28 doi: 10.1515/nleng-2021-0022 – ident: 8 doi: 10.1016/j.cam.2014.01.002 – volume-title: Delay Differential Equations and Applications to Biology year: 2021 ident: 17 doi: 10.1007/978-981-16-0626-7 – ident: 35 doi: 10.3390/math10152581 – ident: 34 doi: 10.3390/sym14010050 – ident: 19 doi: 10.1108/03684920910991540 – ident: 31 doi: 10.3934/math.2023088 – volume-title: Infectious Diseases of Humans: Dynamics and Control year: 1992 ident: 2 – volume: 115 start-page: 700 issue: 772 year: 1927 ident: 3 article-title: A contribution to the mathematical theory of epidemics, Proceedings of the royal society of London. Series A publication-title: Containing papers of a mathematical and physical character – ident: 9 doi: 10.1016/j.cnsns.2010.07.016 – ident: 13 doi: 10.1016/j.chaos.2020.109787 – ident: 30 doi: 10.1016/j.aej.2021.07.020 – ident: 12 doi: 10.1615/critrevbiomedeng.v32.i2.10 – volume-title: Fractional Differential Equations year: 1999 ident: 6 – volume: 354 year: 2022 ident: 16 article-title: Open Problems in Mathematical Biology publication-title: Mathematical Biosciences doi: 10.1016/j.mbs.2022.108926 – volume-title: Mathematical models in epidemiology year: 2019 ident: 24 doi: 10.1007/978-1-4939-9828-9 – volume-title: Introduction to Epidemiology year: 2019 ident: 4 – ident: 10 doi: 10.3390/math10071089 – ident: 27 doi: 10.1140/epjp/s13360-020-01061-9 – ident: 29 doi: 10.1016/j.aej.2022.04.004 – ident: 14 doi: 10.1038/nrg2098 – ident: 26 doi: 10.1016/j.chaos.2020.109957 – volume: 14 start-page: 163 issue: 2 year: 2013 ident: 23 article-title: Approximate solution of SIR infectious disease model using homotopy perturbation method publication-title: Pacific Journal Science and Technology – ident: 18 doi: 10.3390/fractalfract6090490 – ident: 22 doi: 10.1016/j.amc.2009.05.051 – volume-title: Modeling Infectious Diseases in Humans and Animals year: 2008 ident: 1 – ident: 21 doi: 10.3934/math.2023267 – ident: 15 doi: 10.3390/sym14071323 – ident: 33 doi: 10.1155/2022/6939045 – ident: 5 doi: 10.1016/j.chaos.2022.112394 – ident: 32 doi: 10.1016/j.aej.2022.07.022 – volume-title: Dynamical Modeling and Analysis of Epidemics year: 2009 ident: 25 doi: 10.1142/6799 |
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| Snippet | This article presents the solution of the fractional SIR epidemic model using the Laplace residual power series method. We introduce the fractional SIR model... |
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| SubjectTerms | Convergence Differential equations Disease Epidemics Epidemiology Exact solutions Fractional calculus Laplace transforms Mathematical models Numerical analysis Partial differential equations Power series Series expansion Theorems |
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| Title | On the Analytical Solution of Fractional SIR Epidemic Model |
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