  The new coronavirus known as COVID-19 is spread world-wide since December
2019. Without any vaccination or medicine, the means of controlling it are
limited to quarantine and social distancing. Here we study the spatio-temporal
propagation of the first wave of the COVID-19 virus in China and compare it to
other global locations. We provide a comprehensive picture of the spatial
propagation from Hubei to other provinces in China in terms of distance,
population size, and human mobility and their scaling relations. Since strict
quarantine has been usually applied between cities, more insight about the
temporal evolution of the disease can be obtained by analyzing the epidemic
within cities, especially the time evolution of the infection, death, and
recovery rates which affected by policies. We study and compare the infection
rate in different cities in China and provinces in Italy and find that the
disease spread is characterized by a two-stages process. At early times, at
order of few days, the infection rate is close to a constant probably due to
the lack of means to detect infected individuals before infection symptoms are
observed. Then at later times it decays approximately exponentially due to
quarantines. The time evolution of the death and recovery rates also
distinguish between these two stages and reflect the health system situation
which could be overloaded.
