Abstract
The control of Covid 19 epidemics by public health policy in Italy during the first and the second epidemic waves has been driven by using reproductive number Rt(t) to identify the supercritical (percolative), the subcritical (arrested), separated by the critical regime. Here we show that to quantify the Covid-19 spreading rate with containment measures there is a need of a 3D expanded parameter space phase diagram built by the combination of Rt(t) and doubling time Td(t). In this space we identify the Covid-19 dynamics in Italy and its administrative Regions. The supercritical regime is mathematically characterized by (i) the power law of Td vs. [Rt(t) − 1] and (ii) the exponential behaviour of Td vs. time, either in the first and in the second wave. The novel 3D phase diagram shows clearly metastable states appearing before and after the second wave critical regime. for loosening quarantine and tracing of actives cases. The metastable states are precursors of the abrupt onset of a next nascent wave supercritical regime. This dynamic description allows epidemics predictions needed by policymakers interested to point to the target "zero infections" with the elimination of SARS-CoV-2, using the Finding mobile Tracing policy joint with vaccination-campaign, in order to avoid the emergence of recurrent new variants of SARS-CoV-2 virus, accompined by recurrent long lockdowns, with large economical losses, and large number of fatalities.
Highlights
The control of Covid 19 epidemics by public health policy in Italy during the first and the second epidemic waves has been driven by using reproductive number Rt(t) to identify the supercritical, the subcritical, separated by the critical regime
While the laws of uncontrolled epidemics spreading in a single network are well known[1] the quantitative description of the epidemics dynamics in multilayer heterogeneous networks[2] with containment measures is a strategic hot topic for statistical physics of living m atter[3,4,5,6,7,8,9,10] to face Covid-19 pandemic showing non-uniform space population density and short time h eterogeneity[11,12,13,14,15], which give a epidemic dynamics characterized by multiple waves where supercritical phases are intercalated by metastable states in plateaus due to intermittent weakening of the lockdown, quarantine and tracing rules in country enforcing the Lockdown Stop and Go (LSG) p olicy[16,17,18,19]
We have verified the physical laws of the time evolution of the CEwCM using the new 3D expanded parameter space Td(t, Rt) to describe the time evolution of the two Covid-19 epidemic waves, mandatory to face the onset of the third wave
Summary
The control of Covid 19 epidemics by public health policy in Italy during the first and the second epidemic waves has been driven by using reproductive number Rt(t) to identify the supercritical (percolative), the subcritical (arrested), separated by the critical regime. (e) The (Td, Rt, t) 3D phase diagram for Italy (blue) and Germany (red) where the doubling time T d(t, Rt) is plotted vs DOY and the effective reproductive number Rt. here the gray space outlines the critical crossover [40 < T d < 100 days] and separates the supercritical phase [Td < 40 days; Rt > 1] from the arrested subcritical phase [ Td > 100 days; Rt < 1].
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