A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical model
Introduction: Coronavirus COVID-19 pandemic is the defining global health crisis of our time and the greatest challenge we have faced since world war two. To describe this disease mathematically, we noted that COVID-19, due to uncertainties associated to the pandemic, ordinal derivatives and their a...
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| Format: | Article |
| Language: | English |
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Elsevier
2021-09-01
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| Series: | Journal of Advanced Research |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090123220301922 |
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| author | N.H. Sweilam S.M. AL-Mekhlafi D. Baleanu |
| author_facet | N.H. Sweilam S.M. AL-Mekhlafi D. Baleanu |
| author_sort | N.H. Sweilam |
| collection | DOAJ |
| description | Introduction: Coronavirus COVID-19 pandemic is the defining global health crisis of our time and the greatest challenge we have faced since world war two. To describe this disease mathematically, we noted that COVID-19, due to uncertainties associated to the pandemic, ordinal derivatives and their associated integral operators show deficient. The fractional order differential equations models seem more consistent with this disease than the integer order models. This is due to the fact that fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes. Hence there is a growing need to study and use the fractional order differential equations. Also, optimal control theory is very important topic to control the variables in mathematical models of infectious disease. Moreover, a hybrid fractional operator which may be expressed as a linear combination of the Caputo fractional derivative and the Riemann–Liouville fractional integral is recently introduced. This new operator is more general than the operator of Caputo’s fractional derivative. Numerical techniques are very important tool in this area of research because most fractional order problems do not have exact analytic solutions. Objectives: A novel fractional order Coronavirus (2019-nCov) mathematical model with modified parameters will be presented. Optimal control of the suggested model is the main objective of this work. Three control variables are presented in this model to minimize the number of infected populations. Necessary control conditions will be derived. Methods: The numerical methods used to study the fractional optimality system are the weighted average nonstandard finite difference method and the Grünwald-Letnikov nonstandard finite difference method. Results: The proposed model with a new fractional operator is presented. We have successfully applied a kind of Pontryagin’s maximum principle and were able to reduce the number of infected people using the proposed numerical methods. The weighted average nonstandard finite difference method with the new operator derivative has the best results than Grünwald-Letnikov nonstandard finite difference method with the same operator. Moreover, the proposed methods with the new operator have the best results than the proposed methods with Caputo operator. Conclusions: The combination of fractional order derivative and optimal control in the Coronavirus (2019-nCov) mathematical model improves the dynamics of the model. The new operator is more general and suitable to study the optimal control of the proposed model than the Caputo operator and could be more useful for the researchers and scientists. |
| first_indexed | 2024-12-14T00:21:01Z |
| format | Article |
| id | doaj.art-0b921c67341449bebe728120233fbc0b |
| institution | Directory Open Access Journal |
| issn | 2090-1232 |
| language | English |
| last_indexed | 2024-12-14T00:21:01Z |
| publishDate | 2021-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Advanced Research |
| spelling | doaj.art-0b921c67341449bebe728120233fbc0b2022-12-21T23:25:12ZengElsevierJournal of Advanced Research2090-12322021-09-0132149160A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical modelN.H. Sweilam0S.M. AL-Mekhlafi1D. Baleanu2Cairo University, Faculty of Science, Department of Mathematics, Giza, Egypt; Corresponding author.Sana’a University, Faculty of Education, Department of Mathematics, YemenCankaya University, Department of Mathematics, Turkey; Institute of Space Sciences, Magurele-Bucharest, RomaniaIntroduction: Coronavirus COVID-19 pandemic is the defining global health crisis of our time and the greatest challenge we have faced since world war two. To describe this disease mathematically, we noted that COVID-19, due to uncertainties associated to the pandemic, ordinal derivatives and their associated integral operators show deficient. The fractional order differential equations models seem more consistent with this disease than the integer order models. This is due to the fact that fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes. Hence there is a growing need to study and use the fractional order differential equations. Also, optimal control theory is very important topic to control the variables in mathematical models of infectious disease. Moreover, a hybrid fractional operator which may be expressed as a linear combination of the Caputo fractional derivative and the Riemann–Liouville fractional integral is recently introduced. This new operator is more general than the operator of Caputo’s fractional derivative. Numerical techniques are very important tool in this area of research because most fractional order problems do not have exact analytic solutions. Objectives: A novel fractional order Coronavirus (2019-nCov) mathematical model with modified parameters will be presented. Optimal control of the suggested model is the main objective of this work. Three control variables are presented in this model to minimize the number of infected populations. Necessary control conditions will be derived. Methods: The numerical methods used to study the fractional optimality system are the weighted average nonstandard finite difference method and the Grünwald-Letnikov nonstandard finite difference method. Results: The proposed model with a new fractional operator is presented. We have successfully applied a kind of Pontryagin’s maximum principle and were able to reduce the number of infected people using the proposed numerical methods. The weighted average nonstandard finite difference method with the new operator derivative has the best results than Grünwald-Letnikov nonstandard finite difference method with the same operator. Moreover, the proposed methods with the new operator have the best results than the proposed methods with Caputo operator. Conclusions: The combination of fractional order derivative and optimal control in the Coronavirus (2019-nCov) mathematical model improves the dynamics of the model. The new operator is more general and suitable to study the optimal control of the proposed model than the Caputo operator and could be more useful for the researchers and scientists.http://www.sciencedirect.com/science/article/pii/S2090123220301922Coronavirus diseasesA proportional derivativeFractional order optimal control problemsWeighted average nonstandard finite difference methodGrünwald-Letnikov nonstandard finite difference method |
| spellingShingle | N.H. Sweilam S.M. AL-Mekhlafi D. Baleanu A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical model Journal of Advanced Research Coronavirus diseases A proportional derivative Fractional order optimal control problems Weighted average nonstandard finite difference method Grünwald-Letnikov nonstandard finite difference method |
| title | A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical model |
| title_full | A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical model |
| title_fullStr | A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical model |
| title_full_unstemmed | A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical model |
| title_short | A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical model |
| title_sort | hybrid fractional optimal control for a novel coronavirus 2019 ncov mathematical model |
| topic | Coronavirus diseases A proportional derivative Fractional order optimal control problems Weighted average nonstandard finite difference method Grünwald-Letnikov nonstandard finite difference method |
| url | http://www.sciencedirect.com/science/article/pii/S2090123220301922 |
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