Propagation and mitigation of epidemics in a scale-free network

TL;DR

This paper demonstrates that epidemic spread in scale-free networks deviates significantly from traditional SIR model predictions, showing much lower final infection extents and highlighting the importance of targeted mitigation strategies.

Contribution

It provides a counterexample to SIR predictions by analyzing epidemic propagation in scale-free networks, revealing lower infection extents and the effectiveness of targeted quarantining.

Findings

Final epidemic extent is much lower than SIR predictions.

Targeted quarantine of superspreaders is as effective as random mass quarantine.

Daily infection rates are significantly lower than in traditional models.

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.