  COVID-19 is an emerging respiratory infectious disease caused by the
coronavirus SARS-CoV-2. It was first reported on in early December 2019 in
Wuhan, China and within three month spread as a pandemic around the whole
globe. Here, we study macro-epidemiological patterns along the time course of
the pandemic. We compute the distribution of confirmed COVID-19 cases and
deaths for countries worldwide and for counties in the US, and show that both
distributions follow a truncated power-law over five orders of magnitude. We
are able to explain the origin of this scaling behavior as a dual-scale
process: the large-scale spread of the virus between countries and the
small-scale accumulation of case numbers within each country. Assuming
exponential growth on both scales, the critical exponent of the power-law is
determined by the ratio of large-scale to small-scale growth rates. We confirm
this theory in numerical simulations in a simple meta-population model,
describing the epidemic spread in a network of interconnected countries. Our
theory gives a mechanistic explanation why most COVID-19 cases occurred within
a few epicenters, at least in the initial phase of the outbreak. Assessing how
well a simple dual-scale model predicts the early spread of epidemics, despite
the huge contrasts between countries, could help identify critical temporal and
spatial scales of response in which to mitigate future epidemic threats.
