Nonlinear Frequency Analysis of COVID-19 Spread in Tokyo Using Empirical Mode Decomposition

Empirical mode decomposition (EMD) was adopted to decompose daily COVID-19 infections in Tokyo from February 28, 2020, to July 12, 2021. Daily COVID-19 infections were nonlinearly decomposed into several monochromatic waves, intrinsic mode functions (IMFs), corresponding to their periodic meanings from high frequency to low frequency. High-frequency IMFs represent variabilities of random factors and variations in the number of daily PCR and antigen inspections, which can be nonlinearly denoised using EMD. Compared with a moving average and Fourier transform, EMD provides better performance in denoising and analyzing COVID-19 spread. After variabilities of daily inspections were weekly denoised by EMD, one low-frequency IMF reveals that the average period of external influences (public health and social measures) to stop COVID-19 spread was 19 days, corresponding to the measures response duration based on the incubation period. By monitoring this nonlinear wave, public health and social measures for stopping COVID-19 spread can be evaluated and visualized quantitatively in the instantaneous frequency domain. Moreover, another low-frequency IMF revealed that the period of the COVID-19 outbreak and retreat was 57 days on average. This nonlinear wave can be used as a reference for setting the timeframe for state of emergency declarations. Thus, decomposing daily infections in the instantaneous frequency domain using EMD represents a useful tool to improve public health and social measures for stopping COVID-19 spread.