On the analysis of the fractional model of COVID-19 under the piecewise global operators
An expanding field of study that offers fresh and intriguing approaches to both mathematicians and biologists is the symbolic representation of mathematics. In relation to COVID-19, such a method might provide information to humanity for halting the spread of this epidemic, which has severely impact...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/mbe.2023265?viewType=HTML |
| _version_ | 1797900886490480640 |
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| author | M. A. El-Shorbagy Mati ur Rahman Maryam Ahmed Alyami |
| author_facet | M. A. El-Shorbagy Mati ur Rahman Maryam Ahmed Alyami |
| author_sort | M. A. El-Shorbagy |
| collection | DOAJ |
| description | An expanding field of study that offers fresh and intriguing approaches to both mathematicians and biologists is the symbolic representation of mathematics. In relation to COVID-19, such a method might provide information to humanity for halting the spread of this epidemic, which has severely impacted people's quality of life. In this study, we examine a crucial COVID-19 model under a globalized piecewise fractional derivative in the context of Caputo and Atangana Baleanu fractional operators. The said model has been constructed in the format of two fractional operators, having a non-linear time-varying spreading rate, and composed of ten compartmental individuals: Susceptible, Infectious, Diagnosed, Ailing, Recognized, Infectious Real, Threatened, Recovered Diagnosed, Healed and Extinct populations. The qualitative analysis is developed for the proposed model along with the discussion of their dynamical behaviors. The stability of the approximate solution is tested by using the Ulam-Hyers stability approach. For the implementation of the given model in the sense of an approximate piecewise solution, the Newton Polynomial approximate solution technique is applied. The graphing results are with different additional fractional orders connected to COVID-19 disease, and the graphical representation is established for other piecewise fractional orders. By using comparisons of this nature between the graphed and analytical data, we are able to calculate the best-fit parameters for any arbitrary orders with a very low error rate. Additionally, many parameters' effects on the transmission of viral infections are examined and analyzed. Such a discussion will be more informative as it demonstrates the dynamics on various piecewise intervals. |
| first_indexed | 2024-04-10T08:53:07Z |
| format | Article |
| id | doaj.art-1dae1dee658d4b448d0c8471c2fc7046 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-10T08:53:07Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-1dae1dee658d4b448d0c8471c2fc70462023-02-22T01:07:57ZengAIMS PressMathematical Biosciences and Engineering1551-00182023-01-012046134617310.3934/mbe.2023265On the analysis of the fractional model of COVID-19 under the piecewise global operatorsM. A. El-Shorbagy0Mati ur Rahman1Maryam Ahmed Alyami 21. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia 2. Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt3. School of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200030, China4. Department of Mathematics, Faculty of Sciences, University of Jeddah, Jeddah, Saudi ArabiaAn expanding field of study that offers fresh and intriguing approaches to both mathematicians and biologists is the symbolic representation of mathematics. In relation to COVID-19, such a method might provide information to humanity for halting the spread of this epidemic, which has severely impacted people's quality of life. In this study, we examine a crucial COVID-19 model under a globalized piecewise fractional derivative in the context of Caputo and Atangana Baleanu fractional operators. The said model has been constructed in the format of two fractional operators, having a non-linear time-varying spreading rate, and composed of ten compartmental individuals: Susceptible, Infectious, Diagnosed, Ailing, Recognized, Infectious Real, Threatened, Recovered Diagnosed, Healed and Extinct populations. The qualitative analysis is developed for the proposed model along with the discussion of their dynamical behaviors. The stability of the approximate solution is tested by using the Ulam-Hyers stability approach. For the implementation of the given model in the sense of an approximate piecewise solution, the Newton Polynomial approximate solution technique is applied. The graphing results are with different additional fractional orders connected to COVID-19 disease, and the graphical representation is established for other piecewise fractional orders. By using comparisons of this nature between the graphed and analytical data, we are able to calculate the best-fit parameters for any arbitrary orders with a very low error rate. Additionally, many parameters' effects on the transmission of viral infections are examined and analyzed. Such a discussion will be more informative as it demonstrates the dynamics on various piecewise intervals.http://www.aimspress.com/article/doi/10.3934/mbe.2023265?viewType=HTMLcovid-19 modelpiecewise derivative operatorfractional operatorsqualitative analysisnumerical solution |
| spellingShingle | M. A. El-Shorbagy Mati ur Rahman Maryam Ahmed Alyami On the analysis of the fractional model of COVID-19 under the piecewise global operators Mathematical Biosciences and Engineering covid-19 model piecewise derivative operator fractional operators qualitative analysis numerical solution |
| title | On the analysis of the fractional model of COVID-19 under the piecewise global operators |
| title_full | On the analysis of the fractional model of COVID-19 under the piecewise global operators |
| title_fullStr | On the analysis of the fractional model of COVID-19 under the piecewise global operators |
| title_full_unstemmed | On the analysis of the fractional model of COVID-19 under the piecewise global operators |
| title_short | On the analysis of the fractional model of COVID-19 under the piecewise global operators |
| title_sort | on the analysis of the fractional model of covid 19 under the piecewise global operators |
| topic | covid-19 model piecewise derivative operator fractional operators qualitative analysis numerical solution |
| url | http://www.aimspress.com/article/doi/10.3934/mbe.2023265?viewType=HTML |
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