Epidemic spreading in an expanded parameter space: the supercritical scaling laws and subcritical metastable phases

TL;DR

This paper analyzes the COVID-19 epidemic over 230 days using a 3D phase diagram to reveal supercritical scaling laws and subcritical metastable phases, providing a comprehensive physical understanding of epidemic dynamics.

Contribution

It introduces an expanded parameter space with a 3D phase diagram to analyze epidemic data, revealing new scaling laws and metastable phases in the epidemic's progression.

Findings

In the supercritical regime, total infected cases follow Ostwald law growth.

Doubling time follows an exponential law over time.

Subcritical phases exhibit arrested metastability with constant doubling time.

Abstract

So far most of the analysis of coronavirus 2020 epidemic data has been focusing on a short-time window and consequently a quantitative test of statistical physical laws of Coronavirus Epidemics with Containment Measures (CEwCM) is currently lacking. Here we report a quantitative analysis of CEwCM over 230 days, covering the full-time lapse of the first epidemic wave. We use a 3D phase diagram tracking the simultaneous evolution of the doubling time Td(t) and reproductive number Rt(t) showing that this expanded parameter space is needed for biological physics of CEwCP. We have verified that in the supercritical [Rt(t)>1, Td(t)<40 days] regime i) the curve Z(t) of total infected cases follows the growth rate called Ostwald law; ii) the doubling time follows the exponential law Td(t)=A exp((t-t0)/s) as a function of time and iii) the power law Td(t)=C(Rt(t)-1)^-n is verified with the exponent n depending on the definition of Rt(t). The log-log plots Td(t) versus (Rt-1) of the second 2020 epidemic wave unveil in the subcritical regime [Td(t)>100 days] arrested metastable phases with Rt>1 where Td(t) was kept constant followed by its explosion and its containment following the same power law as in the first wave