Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model
In this paper, a hybrid variable-order mathematical model for multi-vaccination COVID-19 is analyzed. The hybrid variable-order derivative is defined as a linear combination of the variable-order integral of Riemann–Liouville and the variable-order Caputo derivative. A symmetry parameter <inline-...
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MDPI AG
2023-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/4/869 |
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| author | Nasser Sweilam Seham M. Al-Mekhlafi Reem G. Salama Tagreed A. Assiri |
| author_facet | Nasser Sweilam Seham M. Al-Mekhlafi Reem G. Salama Tagreed A. Assiri |
| author_sort | Nasser Sweilam |
| collection | DOAJ |
| description | In this paper, a hybrid variable-order mathematical model for multi-vaccination COVID-19 is analyzed. The hybrid variable-order derivative is defined as a linear combination of the variable-order integral of Riemann–Liouville and the variable-order Caputo derivative. A symmetry parameter <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>σ</mi></semantics></math></inline-formula> is presented in order to be consistent with the physical model problem. The existence, uniqueness, boundedness and positivity of the proposed model are given. Moreover, the stability of the proposed model is discussed. The theta finite difference method with the discretization of the hybrid variable-order operator is developed for solving numerically the model problem. This method can be explicit or fully implicit with a large stability region depending on values of the factor <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>Θ</mo></semantics></math></inline-formula>. The convergence and stability analysis of the proposed method are proved. Moreover, the fourth order generalized Runge–Kutta method is also used to study the proposed model. Comparative studies and numerical examples are presented. We found that the proposed model is also more general than the model in the previous study; the results obtained by the proposed method are more stable than previous research in this area. |
| first_indexed | 2024-03-11T04:29:17Z |
| format | Article |
| id | doaj.art-9b8c6cf963394e3c80e8626e19006522 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T04:29:17Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9b8c6cf963394e3c80e8626e190065222023-11-17T21:33:54ZengMDPI AGSymmetry2073-89942023-04-0115486910.3390/sym15040869Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical ModelNasser Sweilam0Seham M. Al-Mekhlafi1Reem G. Salama2Tagreed A. Assiri3Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Education, Sana’a University, Sana’a 1247, YemenDepartment of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62521, EgyptDepartment of mathematics, Faculty of Science, Umm Al-Qura University, Makkah 21961, Saudi ArabiaIn this paper, a hybrid variable-order mathematical model for multi-vaccination COVID-19 is analyzed. The hybrid variable-order derivative is defined as a linear combination of the variable-order integral of Riemann–Liouville and the variable-order Caputo derivative. A symmetry parameter <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>σ</mi></semantics></math></inline-formula> is presented in order to be consistent with the physical model problem. The existence, uniqueness, boundedness and positivity of the proposed model are given. Moreover, the stability of the proposed model is discussed. The theta finite difference method with the discretization of the hybrid variable-order operator is developed for solving numerically the model problem. This method can be explicit or fully implicit with a large stability region depending on values of the factor <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mo>Θ</mo></semantics></math></inline-formula>. The convergence and stability analysis of the proposed method are proved. Moreover, the fourth order generalized Runge–Kutta method is also used to study the proposed model. Comparative studies and numerical examples are presented. We found that the proposed model is also more general than the model in the previous study; the results obtained by the proposed method are more stable than previous research in this area.https://www.mdpi.com/2073-8994/15/4/869variable-order hybrid operatorPfizer vaccineModerna vaccineJanssen vaccinetheta finite difference methodgeneralized fourth order Runge–Kutta method |
| spellingShingle | Nasser Sweilam Seham M. Al-Mekhlafi Reem G. Salama Tagreed A. Assiri Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model Symmetry variable-order hybrid operator Pfizer vaccine Moderna vaccine Janssen vaccine theta finite difference method generalized fourth order Runge–Kutta method |
| title | Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model |
| title_full | Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model |
| title_fullStr | Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model |
| title_full_unstemmed | Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model |
| title_short | Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model |
| title_sort | numerical simulation for a hybrid variable order multi vaccination covid 19 mathematical model |
| topic | variable-order hybrid operator Pfizer vaccine Moderna vaccine Janssen vaccine theta finite difference method generalized fourth order Runge–Kutta method |
| url | https://www.mdpi.com/2073-8994/15/4/869 |
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