4.5 Article

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

Journal

COMPUTATIONAL & APPLIED MATHEMATICS
Volume 40, Issue 3, Pages -

Publisher

SPRINGER HEIDELBERG
DOI: 10.1007/s40314-021-01456-z

Keywords

Fractional calculus; Hysteresis; Mathematical expectation; SIR model; COVID-19

Funding

  1. CNPq [306546/2017-5]
  2. CAPES

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This study explores how hysteresis phenomenon in biological systems can be treated through fractional calculus using a statistical approach, and analyzes the impact of historical values on the evaluation of fractional operators. Additionally, the efficiency of non-integer order calculus is illustrated through the analysis of the dynamics of the spread of COVID-19 in some countries using the SIR compartmental model with and without memory.
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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