Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19
In the present work, a fractional temporal SIR model is considered. The total population is divided into three compartments—susceptible, infected and removed individuals. It generalizes the classical SIR model and consists of three coupled time-fractional ordinary differential equations (ODEs). The...
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MDPI AG
2022-11-01
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| Online Access: | https://www.mdpi.com/2227-7390/10/22/4247 |
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| author | Slavi Georgiev Lubin Vulkov |
| author_facet | Slavi Georgiev Lubin Vulkov |
| author_sort | Slavi Georgiev |
| collection | DOAJ |
| description | In the present work, a fractional temporal SIR model is considered. The total population is divided into three compartments—susceptible, infected and removed individuals. It generalizes the classical SIR model and consists of three coupled time-fractional ordinary differential equations (ODEs). The fractional derivative is introduced to account for the subdiffusion process of confirmed, cured and deceased people dynamics. Although relatively basic, the model is robust and captures the real dynamics, helped by the memory property of the fractional system. In the paper, the issue of an adequate model reconstruction is addressed, and a coefficient identification inverse problem is solved; in particular, the transition and recovering rates, varying in time, are recovered. A least-squares cost functional is minimized for solving the problem. The time-dependent parameters are reconstructed with an iterative predictor–corrector algorithm. Its application is demonstrated via tests with synthetic and real data. What is more, an approach for economic impact assessment is proposed. |
| first_indexed | 2024-03-09T18:10:41Z |
| format | Article |
| id | doaj.art-3c833b583e9f4db79b0629ddbf14af40 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:10:41Z |
| publishDate | 2022-11-01 |
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| spelling | doaj.art-3c833b583e9f4db79b0629ddbf14af402023-11-24T09:08:23ZengMDPI AGMathematics2227-73902022-11-011022424710.3390/math10224247Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19Slavi Georgiev0Lubin Vulkov1Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, BulgariaDepartment of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 7004 Ruse, BulgariaIn the present work, a fractional temporal SIR model is considered. The total population is divided into three compartments—susceptible, infected and removed individuals. It generalizes the classical SIR model and consists of three coupled time-fractional ordinary differential equations (ODEs). The fractional derivative is introduced to account for the subdiffusion process of confirmed, cured and deceased people dynamics. Although relatively basic, the model is robust and captures the real dynamics, helped by the memory property of the fractional system. In the paper, the issue of an adequate model reconstruction is addressed, and a coefficient identification inverse problem is solved; in particular, the transition and recovering rates, varying in time, are recovered. A least-squares cost functional is minimized for solving the problem. The time-dependent parameters are reconstructed with an iterative predictor–corrector algorithm. Its application is demonstrated via tests with synthetic and real data. What is more, an approach for economic impact assessment is proposed.https://www.mdpi.com/2227-7390/10/22/4247COVID-19 outbreakSIR modelingbasic reproduction numberCaputo derivativeeconomic impact |
| spellingShingle | Slavi Georgiev Lubin Vulkov Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19 Mathematics COVID-19 outbreak SIR modeling basic reproduction number Caputo derivative economic impact |
| title | Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19 |
| title_full | Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19 |
| title_fullStr | Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19 |
| title_full_unstemmed | Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19 |
| title_short | Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19 |
| title_sort | numerical coefficient reconstruction of time depending integer and fractional order sir models for economic analysis of covid 19 |
| topic | COVID-19 outbreak SIR modeling basic reproduction number Caputo derivative economic impact |
| url | https://www.mdpi.com/2227-7390/10/22/4247 |
| work_keys_str_mv | AT slavigeorgiev numericalcoefficientreconstructionoftimedependingintegerandfractionalordersirmodelsforeconomicanalysisofcovid19 AT lubinvulkov numericalcoefficientreconstructionoftimedependingintegerandfractionalordersirmodelsforeconomicanalysisofcovid19 |