A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach
The theme of this study is to present the impacts and importance of the fractional order derivatives of the susceptible, infected and quarantine (SIQ) model based on the coronavirus with the lockdown effects. The purpose of these investigations is to achieve more accuracy with the use of fractional...
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MDPI AG
2022-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/3/139 |
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| author | Thongchai Botmart Zulqurnain Sabir Muhammad Asif Zahoor Raja Wajaree Weera Rahma Sadat Mohamed R. Ali |
| author_facet | Thongchai Botmart Zulqurnain Sabir Muhammad Asif Zahoor Raja Wajaree Weera Rahma Sadat Mohamed R. Ali |
| author_sort | Thongchai Botmart |
| collection | DOAJ |
| description | The theme of this study is to present the impacts and importance of the fractional order derivatives of the susceptible, infected and quarantine (SIQ) model based on the coronavirus with the lockdown effects. The purpose of these investigations is to achieve more accuracy with the use of fractional derivatives in the SIQ model. The integer, nonlinear mathematical SIQ system with the lockdown effects is also provided in this study. The lockdown effects are categorized into the dynamics of the susceptible, infective and quarantine, generally known as SIQ mathematical system. The fractional order SIQ mathematical system has never been presented before, nor solved by using the strength of the stochastic solvers. The stochastic solvers based on the Levenberg-Marquardt backpropagation scheme (LMBS) along with the neural networks (NNs), i.e., LMBS-NNs have been implemented to solve the fractional order SIQ mathematical system. Three cases using different values of the fractional order have been provided to solve the fractional order SIQ mathematical model. The data to present the numerical solutions of the fractional order SIQ mathematical model is selected as 80% for training and 10% for both testing and validation. For the correctness of the LMBS-NNs, the obtained numerical results have been compared with the reference solutions through the Adams–Bashforth–Moulton based numerical solver. In order to authenticate the competence, consistency, validity, capability and exactness of the LMB-NNs, the numerical performances using the state transitions (STs), regression, correlation, mean square error (MSE) and error histograms (EHs) are also provided. |
| first_indexed | 2024-03-09T19:49:38Z |
| format | Article |
| id | doaj.art-d605b10c28db44d28a5a37194f9bb16f |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:49:38Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-d605b10c28db44d28a5a37194f9bb16f2023-11-24T01:14:17ZengMDPI AGFractal and Fractional2504-31102022-03-016313910.3390/fractalfract6030139A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical ApproachThongchai Botmart0Zulqurnain Sabir1Muhammad Asif Zahoor Raja2Wajaree Weera3Rahma Sadat4Mohamed R. Ali5Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics and Statistics, Hazara University, Mansehra 21300, PakistanFuture Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, TaiwanDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Zagazig Faculty of Engineering, Zagazig University, Ismailia 44519, EgyptFaculty of Engineering and Technology, Future University, Cairo 11835, EgyptThe theme of this study is to present the impacts and importance of the fractional order derivatives of the susceptible, infected and quarantine (SIQ) model based on the coronavirus with the lockdown effects. The purpose of these investigations is to achieve more accuracy with the use of fractional derivatives in the SIQ model. The integer, nonlinear mathematical SIQ system with the lockdown effects is also provided in this study. The lockdown effects are categorized into the dynamics of the susceptible, infective and quarantine, generally known as SIQ mathematical system. The fractional order SIQ mathematical system has never been presented before, nor solved by using the strength of the stochastic solvers. The stochastic solvers based on the Levenberg-Marquardt backpropagation scheme (LMBS) along with the neural networks (NNs), i.e., LMBS-NNs have been implemented to solve the fractional order SIQ mathematical system. Three cases using different values of the fractional order have been provided to solve the fractional order SIQ mathematical model. The data to present the numerical solutions of the fractional order SIQ mathematical model is selected as 80% for training and 10% for both testing and validation. For the correctness of the LMBS-NNs, the obtained numerical results have been compared with the reference solutions through the Adams–Bashforth–Moulton based numerical solver. In order to authenticate the competence, consistency, validity, capability and exactness of the LMB-NNs, the numerical performances using the state transitions (STs), regression, correlation, mean square error (MSE) and error histograms (EHs) are also provided.https://www.mdpi.com/2504-3110/6/3/139SIQ mathematical modelfractional ordercoronavirusLevenberg-Marquardt backpropagation schemeneural networksAdams–Bashforth–Moulton |
| spellingShingle | Thongchai Botmart Zulqurnain Sabir Muhammad Asif Zahoor Raja Wajaree Weera Rahma Sadat Mohamed R. Ali A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach Fractal and Fractional SIQ mathematical model fractional order coronavirus Levenberg-Marquardt backpropagation scheme neural networks Adams–Bashforth–Moulton |
| title | A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach |
| title_full | A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach |
| title_fullStr | A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach |
| title_full_unstemmed | A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach |
| title_short | A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach |
| title_sort | numerical study of the fractional order dynamical nonlinear susceptible infected and quarantine differential model using the stochastic numerical approach |
| topic | SIQ mathematical model fractional order coronavirus Levenberg-Marquardt backpropagation scheme neural networks Adams–Bashforth–Moulton |
| url | https://www.mdpi.com/2504-3110/6/3/139 |
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