Spatial diffusion process of the COVID-19 Omicron variant epidemic waves in Japan: an application of diffusion non-negative matrix factorisation with human flow

The aim of this study is to understand the geographical diffusion of COVID-19 epidemic waves caused by SARS-CoV-2 Omicron variant in Japan from January 2022 to May 2023. We applied the diffusion non-negative matrix factorisation (diffusion-NMF), which combines a nonnegative matrix factorisation with a spatial weight matrix constructed from human mobility between prefectures, to the cumulative number of COVID-19 positive cases by prefecture. The result showed that the metropolitan centres of Tokyo, Aichi, Osaka and Fukuoka prefectures led the COVID-19 epidemic throughout Japan in the early stage of Omicron waves, followed by hierarchical diffusion to central areas in provincial regions and the no-epicentre stage in subsequent waves.