Scaling analysis of COVID-19 spreading based on Belgian hospitalization data

Bart Smeets; Rodrigo Watte; Herman Ramon

Studies on the outbreak of COVID-19 in the Hubei province and the rest of mainland China show that the temporal evolution of confirmed cases can be classified in three distinct regimes: 1) an initial exponential growth phase, 2) an extended phase of power law growth kinetics indicative of a small world network structure, with a universal growth exponent of µ ≈ 2.1, and 3) a slow inflection to a plateau phase, following a parabolic profile in double logarithmic scale [1] . The roughly quadratic growth can be explained by considering the population as a two-dimensional planar network where the infected population only grows in the periphery of isolated 'patches' of infection [2] . The observed final inflection is not to be confused with the saturation of a logistic growth curve, which arises due to negative feedback as the number of susceptible people decreases with spreading of the infection. This effect is unlikely to contribute in the Chinese case, since even pessimistic estimates of the total number of COVID-19 cases stay very small compared to the total population. More likely, this effect can be attributed to extreme containment measures enacted in China. These measures disconnect the social network structure, producing caging effects that sufficiently slow down the spreading below a reproduction number of 1.