  The COVID-19 pandemic has evolved over time through multiple spatial and
temporal dynamics. The varying extent of interactions among different
geographical areas can result to a complex pattern of spreading so that
influences between these areas can be hard to discern. Here, we use
cross-correlation analysis to detect synchronous evolution and potential
inter-influences in the time evolution of new COVID-19 cases at the county
level in the USA. Our analysis identified two main time periods with
distinguishable features in the behavior of correlations. In the first phase,
there were few strong correlations which only emerged between urban areas. In
the second phase of the epidemic, strong correlations became widespread and
there was a clear directionality of influence from urban to rural areas. In
general, the effect of distance between two counties was much weaker than that
of the counties population. Such analysis can provide possible clues on the
evolution of the disease and may identify parts of the country where
intervention may be more efficient in limiting the disease spread.
