ABSTRACT
The epidemic curve and the final extent of the COVID-19 pandemic are usually predicted from the rate of early exponential raising using the SIR model. These predictions implicitly assume a full social mixing, which is not plausible generally. Here I am showing a counterexample to the these predictions, based on random propagation of an epidemic in Barab\'asi--Albert scale-free network models. The start of the epidemic suggests $R_0=2.6$, but unlike $\Omega\approx 70\%{}$ predicted by the SIR model, they reach a final extent of only $\Omega\approx 4\%{}$ without external mitigation and $\Omega\approx 0.5$--$1.5\%{}$ with mitigation. Daily infection rate at the top is also 1--1.5 orders of magnitude less than in SIR models. Quarantining only the 1.5\%{} most active superspreaders has similar effect on extent and top infection rate as blind quarantining a random 50\%{} of the full community.