The coronavirus known as COVID-19 has spread worldwide 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 into 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 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. In early times, of the 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. This exponential decay allows us to define a characteristic time of controlling the disease which we found to be approximately 20 days for most cities in China in marked contrast to different provinces in Italy which are characterized with much longer controlling time indicating less efficient controlling policies. Moreover, we study the time evolution of the death and recovery rates which we found to show similar behavior as the infection rate and reflect the health system situation which could be overloaded.

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.

We study a spatial network model with exponentially distributed link-lengths on an underlying grid of points, undergoing a structural crossover from a random, Erdős-Rényi graph to a 2D lattice at the characteristic interaction range ζ. We find that, whilst far from the percolation threshold the random part of the incipient cluster scales linearly with ζ, close to criticality it extends in space until the universal length scale ζ 3/2 before crossing over to the spatial one. We demonstrate this critical stretching phenomenon in percolation and in dynamical processes, and we discuss its implications to real-world phenomena, such as neural activation, traffic flows or epidemic spreading.

We study a realistic spatial network model constructed by randomly linking lattice sites with linklengths following an exponential distribution with a characteristic scale ζ. We find that this simple spatial network topology does not fulfill any single universality class, but exhibits a new multiuniversality with two sets of critical exponents. This bi-universality is characterized by random-like scaling laws for measurements on a scale smaller than ζ but spatial scaling for measurements on a larger scale. We further explore this topology by studying the resilience of a two-layer multiplex under localized attack. We find that for a broad range of the control parameters, our system is metastable. In this metastable region, a localized attack larger than a critical size -that does not depends on the size of the system -induces a propagating cascade of failures leading to the system collapse.

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