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, 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.

Automated summary

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.