Sars-Cov2 world pandemic recurrent waves controlled by variants evolution and vaccination campaign.

While understanding the time evolution of Covid-19 pandemic is needed to plan economics and tune sanitary policies, a quantitative information of the recurrent epidemic waves is elusive. This work describes a statistical physics study of the subsequent waves in the epidemic spreading of Covid-19 and disclose the frequency components of the epidemic waves pattern over two years in United States, United Kingdom and Japan. These countries have been taken as representative cases of different containment policies such as "Mitigation" (USA and UK) and "Zero Covid" (Japan) policies. The supercritical phases in spreading have been identified by intervals with RIC-index > 0. We have used the wavelet transform of infection and fatality waves to get the spectral analysis showing a dominant component around 130 days. Data of the world dynamic clearly indicates also the crossover to a different phase due to the enforcement of vaccination campaign. In Japan and United Kingdom, we observed the emergence in the infection waves of a long period component (~ 170 days) during vaccination campaign. These results indicate slowing down of the epidemic spreading dynamics due to the vaccination campaign. Finally, we find an intrinsic difference between infection and fatality waves pointing to a non-trivial variation of the lethality due to different gene variants.

Periodic recurrent waves of Covid-19 epidemics and vaccination campaign.

While understanding of periodic recurrent waves of Covid-19 epidemics would aid to combat the pandemics, quantitative analysis of data over a two years period from the outbreak, is lacking. The complexity of Covid-19 recurrent waves is related with the concurrent role of i) the containment measures enforced to mitigate the epidemics spreading ii) the rate of viral gene mutations, and iii) the variable immune response of the host implemented by vaccination. This work focuses on the effect of massive vaccination and gene variants on the recurrent waves in a representative case of countries enforcing mitigation and vaccination strategy. The spreading rate is measured by the ratio between the reproductive number Rt(t) and the doubling time Td(t) called RIC-index and the daily fatalities number. The dynamics of the Covid-19 epidemics have been studied by wavelet analysis and represented by a non-linear helicoid vortex in a 3D space where both RIC-index and fatalities change with time. The onset of periodic recurrent waves has been identified by the transition from convergent to divergent trajectories on the helicoid vortex. We report a main period of recurrent waves of 120 days and the elongation of this period after the vaccination campaign.

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 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.

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

While the mathematical laws of uncontrolled epidemic spreading are well known, the statistical physics of coronavirus epidemics with containment measures is currently lacking. The modelling of available data of the first wave of the Covid-19 pandemic in 2020 over 230 days, in different countries representative of different containment policies is relevant to quantify the efficiency of these policies to face the containment of any successive wave. At this aim we have built a 3D phase diagram tracking the simultaneous evolution and the interplay of the doubling time,Td, and the reproductive number,Rtmeasured using the methodological definition used by the Robert Koch Institute. In this expanded parameter space three different main phases,supercritical,criticalandsubcriticalare identified. Moreover, we have found that in thesupercriticalregime withRt> 1 the doubling time is smaller than 40 days. In this phase we have established the power law relation betweenTdand (Rt- 1)-νwith the exponentνdepending on the definition of reproductive number. In thesubcriticalregime whereRt< 1 andTd> 100 days, we have identified arrested metastable phases whereTdis nearly constant.

Ostwald Growth Rate in Controlled Covid-19 Epidemic Spreading as in Arrested Growth in Quantum Complex Matter

Here, we focus on the data analysis of the growth of epidemic spread of Covid-19 in countries where different policies of containment were activated. It is known that the growth of pandemic spread at its threshold is exponential, but it is not known how to quantify the success of different containment policies. We identify that a successful approach gives an arrested phase regime following the Ostwald growth, where, over the course of time, one phase transforms into another metastable phase with a similar free energy as observed in oxygen interstitial diffusion in quantum complex matter and in crystallization of proteins. We introduce the s factor which provides a quantitative measure of the efficiency and speed of the adopted containment policy, which is very helpful not only to monitor the Covid-19 pandemic spread but also for other countries to choose the best containment policy. The results show that a policy based on joint confinement, targeted tests, and tracking positive cases is the most rapid pandemic containment policy;in fact, we found values of 9, 5, and 31 for the success s factor for China, South Korea, and Italy, respectively, where the lowest s factor indicates the best containment policy.

Efficiency of COVID-19 mobile contact tracing containment by measuring time-dependent doubling time.

The COVID-19 epidemic of the novel coronavirus (severe acute respiratory syndrome SARS-CoV-2) has spread around the world. While different containment policies using non-pharmaceutical interventions have been applied, their efficiencies are not known quantitatively. We show that the doubling time T d(t) with the success s factor, the characteristic time of the exponential growth of T d(t) in the arrested regime, is a reliable tool for early predictions of epidemic spread time evolution and provides a quantitative measure of the success of different containment measures. The efficiency of the containment policy lockdown case finding mobile tracing (LFT) using mandatory mobile contact tracing is much higher than that of the lockdown stop and go policy proposed by the Imperial College team in London. A very low s factor was reached by the LFT policy, giving the shortest time width of the positive case curve and the lowest number of fatalities. The LFT policy was able to reduce the number of fatalities by a factor of 100 in the first 100 d of the COVID-19 epidemic, reduce the time width of the COVID-19 pandemic curve by a factor 2.5, and rapidly stop new outbreaks and thereby avoid a second wave to date.