Universal scaling of human flow remain unchanged during the COVID-19 pandemic.

To prevent the spread of the COVID-19 pandemic, governments in various countries have severely restricted the movement of people. The large amount of detailed human location data obtained from mobile phone users is useful for understanding the change of flow patterns of people under the effect of pandemic. In this paper, we observe the synchronized human flow during the COVID-19 pandemic using Global Positioning System data of about 1 million people obtained from mobile phone users. We apply the drainage basin analysis method which we introduced earlier for characterization of macroscopic human flow patterns to observe the effect of the spreading pandemic. Before the pandemic the afternoon basin size distribution has been approximated by an exponential distribution, however, the distribution of Tokyo and Sapporo, which were most affected by the first wave of COVID-19, deviated significantly from the exponential distribution. On the other hand, during the morning rush hour, the scaling law holds universally, i.e., in all cities, even though the number of moving people in the basin has decreased significantly. The fact that these scaling laws, which are closely related to the three-dimensionality structure of the city and the fractal structure of the transportation network, have not changed indicates that the macroscopic human flow features are determined mainly by the means of transport and the basic structure of cities which are invariant of the pandemic.