The memory effect on fractional calculus: an application in the spread of COVID-19

• Published in: Computational & applied mathematics Vol. 40; no. 3
• Main Authors: Barros, Laécio Carvalho de, Lopes, Michele Martins, Pedro, Francielle Santo, Esmi, Estevão, Santos, José Paulo Carvalho dos, Sánchez, Daniel Eduardo
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2021; Springer Nature B.V
• Subjects: 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); COVID-19; Mathematical expectation; SIR model; Fractional calculus; Hysteresis
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-021-01456-z

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.