Numerical treatments for the optimal control of two types variable-order COVID-19 model
In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable-order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-11-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722005782 |
| _version_ | 1798029274171572224 |
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| author | Nasser Sweilam Seham Al-Mekhlafi Salma Shatta Dumitru Baleanu |
| author_facet | Nasser Sweilam Seham Al-Mekhlafi Salma Shatta Dumitru Baleanu |
| author_sort | Nasser Sweilam |
| collection | DOAJ |
| description | In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable-order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge–Kutta method and the non-standard generalized fifth-order Runge–Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies’ simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown. |
| first_indexed | 2024-04-11T19:21:34Z |
| format | Article |
| id | doaj.art-eb0b6550fcce4f20a9c70102223a417e |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-11T19:21:34Z |
| publishDate | 2022-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-eb0b6550fcce4f20a9c70102223a417e2022-12-22T04:07:17ZengElsevierResults in Physics2211-37972022-11-0142105964Numerical treatments for the optimal control of two types variable-order COVID-19 modelNasser Sweilam0Seham Al-Mekhlafi1Salma Shatta2Dumitru Baleanu3Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt; Corresponding author.Department of Mathematics, Faculty of Education, Sana’a University, Yemen; Department of Engineering Mathematics and Physics, Future University in Egypt, EgyptDepartment of Mathematics, Faculty of Science, Helwan University, Cairo, EgyptCankaya University, Department of Mathematics, Turkey; Institute of Space Sciences, Magurele-Bucharest, RomaniaIn this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable-order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge–Kutta method and the non-standard generalized fifth-order Runge–Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies’ simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown.http://www.sciencedirect.com/science/article/pii/S2211379722005782COVID-19 epidemic modelsCaputo’s derivativesOptimal control theoryStability analysisNon-standard generalized Runge–Kutta methods |
| spellingShingle | Nasser Sweilam Seham Al-Mekhlafi Salma Shatta Dumitru Baleanu Numerical treatments for the optimal control of two types variable-order COVID-19 model Results in Physics COVID-19 epidemic models Caputo’s derivatives Optimal control theory Stability analysis Non-standard generalized Runge–Kutta methods |
| title | Numerical treatments for the optimal control of two types variable-order COVID-19 model |
| title_full | Numerical treatments for the optimal control of two types variable-order COVID-19 model |
| title_fullStr | Numerical treatments for the optimal control of two types variable-order COVID-19 model |
| title_full_unstemmed | Numerical treatments for the optimal control of two types variable-order COVID-19 model |
| title_short | Numerical treatments for the optimal control of two types variable-order COVID-19 model |
| title_sort | numerical treatments for the optimal control of two types variable order covid 19 model |
| topic | COVID-19 epidemic models Caputo’s derivatives Optimal control theory Stability analysis Non-standard generalized Runge–Kutta methods |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722005782 |
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