  The global spread of the COVID-19 pandemic has followed complex pathways,
largely attributed to the high virus infectivity, human travel patterns, and
the implementation of multiple mitigation measures. The resulting geographic
patterns describe the evolution of the epidemic and can indicate areas which
are at risk of an outbreak. Here, we analyze the spatial correlations of new
active cases in USA at the county level and characterize the extent of these
correlations at different times. We show that the epidemic did not progress
uniformly and we identify various stages which are distinguished by significant
differences in the correlation length. Our results indicate that the
correlation length may be large even during periods when the number of cases
declines. We find that correlations between urban centers were much more
significant than between rural areas and this finding indicates that long-range
spreading was mainly facilitated by travel between cities, especially at the
first months of the epidemic. We also show the existence of a percolation
transition in November 2020, when the largest part of the country was connected
to a spanning cluster, and a smaller-scale transition in January 2021, with
both times corresponding to the peak of the epidemic in the country.
