Analysis of non-equilibrium fluctuations in a number of COVID-19 cases and deaths based on time-convolutionless projection-operator method

TL;DR

This paper analyzes COVID-19 case and death fluctuations using advanced stochastic methods, transforming complex multiplicative noise into a Langevin equation to better understand the underlying dynamics and similarities in case and death patterns.

Contribution

It introduces a novel application of the time-convolutionless projection-operator method to model COVID-19 fluctuations, transforming multiplicative noise into an additive Langevin form.

Findings

Fluctuations are described by a stochastic equation with multiplicative noise.

The method transforms this into a Langevin equation with additive noise.

Deaths and cases show similar dynamical behavior in fluctuations.

Abstract

The non-equilibrium fluctuations observed in a number of COVID-19 cases and deaths are analyzed from a statistical-dynamical point view. By investigating the data observed around the world which were collected from January 15, 2020 to April 28, 2023 at https://coronavirus.jhu.edu/, we first show that the dynamics of the fluctuations is described by a stochastic equation whose stochastic force is a multiplicative type. By employing the time-convolutionless projection-operator method in open systems previously proposed by the present author, we then transform it into a Langevin-type equation with an additive-type stochastic force together with the corresponding Fokker-Planck type equation. Thus, we explore the stochastic properties of a Langevin-type stochastic force not only analytically but also numerically from a unified point of view. Finally, we emphasize that the dynamical behavior in deaths resembles that in cases very much not only for the causal motion but also for the fluctuation.