  Revealing spatiotemporal evolution regularity in the spatial diffusion of
epidemics is helpful for preventing and controlling the spread of epidemics.
Based on the real-time COVID-19 datasets by prefecture-level cities, this paper
is devoted to exploring the multifractal scaling in spatial diffusion pattern
of COVID-19 pandemic and its evolution characteristics in Chinese mainland. The
ArcGIS technology and box-counting method are employed to extract spatial data
and the least square regression based on rescaling probability (miu-weight
method) is used to calculate fractal parameters. The results show multifractal
distribution of COVID-19 pandemic in China. The generalized correlation
dimension spectrums are inverse S-shaped curves, but the fractal dimension
values significantly exceed the Euclidean dimension of embedding space when
moment order q<<0. The local singularity spectrums are asymmetric unimodal
curves, which slant to right. The fractal dimension growth curves are shown as
quasi S-shaped curves. From these spectrums and growth curves, the main
conclusions can be drawn as follows: First, self-similar patterns developed in
the process of COVID-19 pandemic, which seem be dominated by multifractal
scaling law. Second, the spatial pattern of COVID-19 across China can be
characterized by global clustering with local disordered diffusion. Third, the
spatial diffusion process of COVID-19 in China experienced four stages, i.e.,
initial stage, the rapid diffusion stage, the hierarchical diffusion stage, and
finally the contraction stage. This study suggests that multifractal theory can
be utilized to characterize spatio-temporal diffusion of COVID-19 pandemic, and
the case analyses may be instructive for further exploring natural laws of
spatial diffusion.
