Spectral study of COVID-19 pandemic in Japan: The dependence of spectral gradient on the population size of the community

Abstract

We have carried out spectral analysis of coronavirus disease 2019 (COVID-19) notifications in all 47 prefectures in Japan. The results confirm that the power spectral densities (PSDs) of the data from each prefecture show exponential characteristics, which are universally observed in the PSDs of time series generated by nonlinear dynamical systems, such as the susceptible/exposed/infectious/recovered (SEIR) epidemic model. The exponential gradient increases with the population size. For all prefectures, many spectral lines observed in each PSD can be fully assigned to a fundamental mode and its harmonics and subharmonics, or linear combinations of a few fundamental periods, suggesting that the COVID-19 data are substantially noise-free. For prefectures with large population sizes, PSD patterns obtained from segment time series behave in response to the introduction of public and workplace vaccination programs as predicted by theoretical studies based on the SEIR model. The meaning of the relationship between the exponential gradient and the population size is discussed.