Metastable states in plateaus and multi-wave epidemic dynamics of Covid-19 spreading in Italy

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 R(t)(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 R(t)(t) and doubling time T(d)(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 T(d) vs. [R(t)(t) − 1] and (ii) the exponential behaviour of T(d) 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.