A fractional-order generalized Richards growth model and its implementation to COVID-19 data
In this article, we include the memory effect in the generalized Richards model (GRM), which is proposed in the form of a fractional-order GRM. The fractional-order GRM is developed by replacing the first-order derivative in the GRM with a fractional-order derivative and then taking care of model ho...
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Taylor & Francis Group
2024-12-01
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Series: | Arab Journal of Basic and Applied Sciences |
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Online Access: | https://www.tandfonline.com/doi/10.1080/25765299.2024.2362987 |
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author | Agus Suryanto Isnani Darti Trisilowati Bapan Ghosh Raqqasyi Rahmatullah Musafir |
author_facet | Agus Suryanto Isnani Darti Trisilowati Bapan Ghosh Raqqasyi Rahmatullah Musafir |
author_sort | Agus Suryanto |
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description | In this article, we include the memory effect in the generalized Richards model (GRM), which is proposed in the form of a fractional-order GRM. The fractional-order GRM is developed by replacing the first-order derivative in the GRM with a fractional-order derivative and then taking care of model homogeneity of dimension. We consider two fractional-order differential operators: Caputo and Atangana–Baleanu in the Caputo sense (ABC). The proposed fractional-order models are then implemented to fit the COVID-19 data in East Java, Indonesia from March 25 until October 31, 2020. The fitting is performed by minimizing the sum of the squared residual between the numerical solutions of each fractional-order model and the daily data of a cumulative number of COVID-19 cases. The numerical solutions of both fractional-order models are determined by the predictor-corrector method. The performance of the two fractional models is measured by two performance metrics: coefficient of determination (R2) and root mean square error (RMSE). By considering that the order of fractional derivative as an extra degree of freedom, we perform data fitting for several orders of fractional derivative and evaluate the two performance metrics. It is observed that the fractional-order model with the ABC operator generally has the best performance in calibrating and forecasting both the cumulative number of COVID-19 cases and daily new cases of COVID-19. |
format | Article |
id | doaj-art-6ea03b466c6b45f19e91267cead9dc6c |
institution | Kabale University |
issn | 2576-5299 |
language | English |
publishDate | 2024-12-01 |
publisher | Taylor & Francis Group |
record_format | Article |
series | Arab Journal of Basic and Applied Sciences |
spelling | doaj-art-6ea03b466c6b45f19e91267cead9dc6c2024-12-17T08:04:46ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992024-12-0131134535710.1080/25765299.2024.2362987A fractional-order generalized Richards growth model and its implementation to COVID-19 dataAgus Suryanto0Isnani Darti1 Trisilowati2Bapan Ghosh3Raqqasyi Rahmatullah Musafir4Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, IndonesiaDifferential Equations, Modeling, and Simulation Group, Department of Mathematics, Indian Institute of Technology Indore, Madhya Pradesh, IndiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, IndonesiaIn this article, we include the memory effect in the generalized Richards model (GRM), which is proposed in the form of a fractional-order GRM. The fractional-order GRM is developed by replacing the first-order derivative in the GRM with a fractional-order derivative and then taking care of model homogeneity of dimension. We consider two fractional-order differential operators: Caputo and Atangana–Baleanu in the Caputo sense (ABC). The proposed fractional-order models are then implemented to fit the COVID-19 data in East Java, Indonesia from March 25 until October 31, 2020. The fitting is performed by minimizing the sum of the squared residual between the numerical solutions of each fractional-order model and the daily data of a cumulative number of COVID-19 cases. The numerical solutions of both fractional-order models are determined by the predictor-corrector method. The performance of the two fractional models is measured by two performance metrics: coefficient of determination (R2) and root mean square error (RMSE). By considering that the order of fractional derivative as an extra degree of freedom, we perform data fitting for several orders of fractional derivative and evaluate the two performance metrics. It is observed that the fractional-order model with the ABC operator generally has the best performance in calibrating and forecasting both the cumulative number of COVID-19 cases and daily new cases of COVID-19.https://www.tandfonline.com/doi/10.1080/25765299.2024.2362987Adams–Bashforth–Moulton schemeAtangana–Baleanu–Caputo fractional derivativeCaputo fractional derivativefractional growth modelparameter estimation |
spellingShingle | Agus Suryanto Isnani Darti Trisilowati Bapan Ghosh Raqqasyi Rahmatullah Musafir A fractional-order generalized Richards growth model and its implementation to COVID-19 data Arab Journal of Basic and Applied Sciences Adams–Bashforth–Moulton scheme Atangana–Baleanu–Caputo fractional derivative Caputo fractional derivative fractional growth model parameter estimation |
title | A fractional-order generalized Richards growth model and its implementation to COVID-19 data |
title_full | A fractional-order generalized Richards growth model and its implementation to COVID-19 data |
title_fullStr | A fractional-order generalized Richards growth model and its implementation to COVID-19 data |
title_full_unstemmed | A fractional-order generalized Richards growth model and its implementation to COVID-19 data |
title_short | A fractional-order generalized Richards growth model and its implementation to COVID-19 data |
title_sort | fractional order generalized richards growth model and its implementation to covid 19 data |
topic | Adams–Bashforth–Moulton scheme Atangana–Baleanu–Caputo fractional derivative Caputo fractional derivative fractional growth model parameter estimation |
url | https://www.tandfonline.com/doi/10.1080/25765299.2024.2362987 |
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