The memory effect on fractional calculus: an application in the spread of COVID-19
Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest of this work is to attest, through a statistical approach, how the hysteresis phenomenon, which describes a type of memory effect present in biological systems,...
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| Published in | Computational & applied mathematics Vol. 40; no. 3 |
|---|---|
| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.04.2021
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2238-3603 1807-0302 |
| DOI | 10.1007/s40314-021-01456-z |
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| Abstract | Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest of this work is to attest, through a statistical approach, how the hysteresis phenomenon, which describes a type of memory effect present in biological systems, can be treated by fractional calculus. We also analyse the contribution of the historical values of a function in the evaluation of fractional operators according to their order. To illustrate the efficiency of this non-integer order calculus, we consider the SIR (susceptible–infected–recovered) compartmental model which is widely used in epidemiology. We employ this compartmental model to study the dynamics of the spread of COVID-19 in some countries, one version with memory and one without memory. |
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| AbstractList | Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest of this work is to attest, through a statistical approach, how the hysteresis phenomenon, which describes a type of memory effect present in biological systems, can be treated by fractional calculus. We also analyse the contribution of the historical values of a function in the evaluation of fractional operators according to their order. To illustrate the efficiency of this non-integer order calculus, we consider the SIR (susceptible–infected–recovered) compartmental model which is widely used in epidemiology. We employ this compartmental model to study the dynamics of the spread of COVID-19 in some countries, one version with memory and one without memory. |
| ArticleNumber | 72 |
| Author | Lopes, Michele Martins Barros, Laécio Carvalho de Santos, José Paulo Carvalho dos Sánchez, Daniel Eduardo Pedro, Francielle Santo Esmi, Estevão |
| Author_xml | – sequence: 1 givenname: Laécio Carvalho de surname: Barros fullname: Barros, Laécio Carvalho de organization: Department of Applied Mathematics, University of Campinas – sequence: 2 givenname: Michele Martins orcidid: 0000-0002-9539-4916 surname: Lopes fullname: Lopes, Michele Martins email: mi_martins22@hotmail.com organization: Department of Applied Mathematics, University of Campinas – sequence: 3 givenname: Francielle Santo surname: Pedro fullname: Pedro, Francielle Santo organization: Multidisciplinary Department, Federal University of São Paulo – sequence: 4 givenname: Estevão surname: Esmi fullname: Esmi, Estevão organization: Department of Applied Mathematics, University of Campinas – sequence: 5 givenname: José Paulo Carvalho dos surname: Santos fullname: Santos, José Paulo Carvalho dos organization: Department of Mathematics, Federal University of Alfenas – sequence: 6 givenname: Daniel Eduardo surname: Sánchez fullname: Sánchez, Daniel Eduardo organization: Center of Basic Science Teaching for Engineering, University Austral of Chile |
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| Keywords | COVID-19 Mathematical expectation SIR model Fractional calculus Hysteresis |
| Language | English |
| License | This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
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| SubjectTerms | Applications of Mathematics Applied physics Biological effects Calculus Computational mathematics Computational Mathematics and Numerical Analysis Coronaviruses COVID-19 Epidemiology Fractional calculus Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics Operators (mathematics) |
| Title | The memory effect on fractional calculus: an application in the spread of COVID-19 |
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