  Epidemics unfold by means of a spreading process from each infected
individual to a random number of secondary cases. It has been claimed that the
so-called superspreading events in COVID-19 are governed by a power-law tailed
distribution of secondary cases, with no finite variance. Using a
continuous-time branching process, we show that for such power-law
superspreading the survival probability of an outbreak as a function of time
and the basic reproductive number fulfills a "finite-time scaling" law
(analogous to finite-size scaling) with universal-like characteristics only
dependent on the power-law exponent. This clearly shows how the phase
transition separating a subcritical and a supercritical phase emerges in the
infinite-time limit (analogous to the thermodynamic limit). We quantify the
counterintuitive hazards infinite-variance superspreading poses and conclude
that superspreading only leads to new phenomenology in the infinite-variance
case.
