*Epidemics trend in Italy and Lombardia region.*

Table 1 shows the dynamics of the RI index (dH/dI, calculated as the average value at different time intervals both in Lombardia and in the rest of Italy). The different time intervals (“fields”) correspond to the peculiar behaviour of infectious dynamics, analyzed for Lombardia and for the rest of other Italian regions. Raw data have been provided by daily sampling made by Italian Health Administration and are affected by biases due to non random sampling and test uncertainty (especially important in the first phases of the epidemic).

With a simple glance at Table 1, it is possible to appreciate the differences between Lombardia and the rest of the Italian regions. The difference is evident from the average values of RI = dH/dI calculated for each field, between T0 and T5. The first field highlights an RI greater in Lombardia with respect to the rest of Italy tracking the start of the epidemic process in this region. Consistently, the much higher percentage of patients healed in Lombardia region in the initial periods suggests the need to bring the actual start of the process back in time compared to the official registration of the first cases. Going to more recent times (successive intervals) is evident as the index reaches a plateau at window T3 for ’rest of Italy’, indicating the end of the cycle of epidemic, while still floating in Lombardia, with a large dispersion of the RI value .This is still more evident in Figures 1A and 1B.

Figure 1A reports daily changes since 24 February 2020 (T0), of infected, and healed in Italy without Lombardia. Top panel reports RI (dH/dI) index while bottom panel refers to the temporal trend of healed and infected cases. The analysis of single sections of the time course suggest some interesting observations. The average RI value in Field 1 T0-T1 is near to zero; there is only a slow increase of infected (it must be remembered the low number of swap analyses performed in this period) with almost non-detectable increase of healed cases. The average RI value in the Field 2 T1-T2 is on the rise, but lower than 1 due to the temporal delay between healed and infected cases generation. The infection rate rises, and so does healed curve but at a lower rate. The average RI value reaches a ‘tipping point’ marking a phase transition11 of the dynamics at Field 3 (T2-T3). The healed daily variation overcomes the infection rate and the RI has a huge variance, another signature of phase transition11. In this time interval, the Infection rate reaches its plateau while healed curve displays a neat acceleration. The average value RI assumes an average value >1 in the Field 4 (T3-T4), where a significant departure of the rate in between healed and infected patients can be observed. Finally, in the Field 5 (T4-T5), the dH/dI ratio assumes an average value <0. From this point onward, dH/dI is no more relevant given the negative rate of infected persons and thus the negative values of dH/dI index. This is a further proof of the phase transition started in the previous intervals and identified by infection peak. It is worth noting how the two extremes of the section (3 and 16 April) are coincident with the reduction of the absolute number of infected persons. This behaviour coincides with the plateau of our forward model based on a completely independent approach.

Figure 1B relates to the Lombardia region and tells us a different story than the rest of Italy. First, we note that, in contrast to the rest of Italy, there is no clear "critical point". The RI does not assume the average value >1 for the entire range of data examined (82 days from T0 corresponding to 12 May 2020), while in the rest of Italy the number of recovered people is very high, with RI> 1 starting from the 40th day (April 2, 2020). The Lombardia region continues to oscillate around an average index of RI=0.65, without reaching a stable plateau or going towards stable negative territories. All in all, the proposed index tells us of the reaching of a tipping-point at day 45 from the beginning of analysis (in the rest of Italy) that marks the end of epidemic cycle being the fatalities after that point the ‘echo’ of previous infections. Lombardia differs from the previous sketched scenario as it displays a completely different dynamics of the index.

*Parameters for clinical severity estimation*

The aforementioned Japan/Italy paradox, where two nations with largely super- imposable demographic structures have huge differences in lethality trends, asks for something different from the usual lethality indexes. We decide to remove the principal cause of uncertainty, i.e. the rate of infected people, by focusing on different observables. That goal was achieved by relying on the relation between the number of accesses in intensive care units (ICU) and the number of deaths. Both these variables are known with no (or very little) uncertainty and they give an immediate estimate of the severity of the disease (Fig.2A, B).

Figures 2C and 2D reports the evolution of ICU as well as the Covid-19-related fatalities recorded on a daily basis in Italy, excluding (Fig.2C) and including Lombardia data (Fig. 2D). Figure 2C shows the parallel behavior of the number of accesses to intensive care and the number of deaths for the entire country. The two parameters are strictly correlated (Pearson r = 0.94), and the slope of the curve is equal to 0.19 pointing to an 81% of success for intensive care (Figure 2a). This relation points to a constant ‘clinical relevance’ of the disease throughout the entire time course.

The figure refers to the same day for both death numbers and ICUs and is worth noting that the fit comes from the shared trend of the two variables both registering the same epidemic spread. As a matter of fact the ‘lagged correlations’ (i.e. the correlations between number of deaths and ICUs, three, four, five and six days before) displayed a significantly lower correlation coefficient. The fact that ICUs- Fatalities relation is driven by the epidemics dynamics (the relation practically disappears when lagged correlations are computed) tells us that this relation can be considered as a proxy of the epidemics dynamics more than a purely clinical descriptor. Figures 2C and 2D describe the simultaneous evolution over time of the two parameters – ICUs and death – evidencing how the rise and the subsequent decline of the epidemics can aptly be depicted with the help of these observables. Keeping in mind that fatalities have a variable delay from hospitalization, the ICUs- Dead number function is equivalent to a temporal differential rate of infection scaled by a largely constant intrinsic fatality rate. At odds with other strategies, the ICUs- Dead number function does not imply any direct infection estimate.

Figure 2B refers to Lombardia, and again we observe a strict relation between the number of daily accesses to intensive care units and deaths. It is worth noting that while for the rest of Italy the slope was 0.19, the slope relative to Lombardia is quite higher (0.28) pointing to a decreased success of care dropping from 81 to 72%. By a closer look at Fig.2B is evident how the right part of the plot (corresponding to the peak of the epidemics with higher number of both fatalities and intensive care accesses) has a higher displacement of observations from the regression line with a tendency to score a higher number of fatalities.

This asymmetric displacement could be the image in light of the initial overcrowding of the hospitals in Lombardia that first faced the initial impact of the epidemic. In any case, the relation between hospital accesses and deaths can be considered as a useful parameter for monitoring disease severity. The corollary of this fact is that the number of healed individuals properly reflects the epidemics evolution in a clinically reasonable way, allowing overcoming bias provided by uncorrected data collection about incidence and lethality. Accesses to critical care units reach a peak at mid- March and then regularly decreases, reaching in these days (July 2020) very limited numbers (<50 patients in respect to ~4000 at mid March). We hypothesize that this behaviour reflects the improvement in treatment of patients that are followed at home or in standard hospital regimen, and does not imply any change in the viral pathogenicity, at least in the short period we have investigated.

These findings bring some relevant consequences: a) despite infection and death rates values being untrustworthy, recording of critical care units accesses rates can provide a useful estimate of epidemic dynamics, especially if we aim to appreciate the most relevant medical outcomes; b) decrease in critical care units accesses rates mirrors the ones we observed for death rates.

Given the reduction in hospitalization in intensive care structures is mostly ascribed to improved efficiency of medical treatments delivered at home or during standard hospitalization, it can be reliably surmised that early and efficient pharmacological therapy can successfully reduce both accesses to critical care units as well as death rates. While the reasons behind the (apparent) high incidence of fatality rates in Lombardia still remain uncovered, we can exclude that differences in virus pathogenicity could provide an affordable answer. The impressive trend we observed in Lombardia from the outset (end of February 2020) simply demonstrated that, since the beginning, the number of (asymptomatic) infected individuals reached a “critical” mass that ultimately caused a sudden “eruption”. Indeed, almost half of the Covid-19 cases registered in Italy occurred in Lombardia.

The Verhulst-Pearle sigmoid model (sigmoid) (Fig. 3A, B) allowed us to reconstruct the time and intensity of the epidemics peak and to highlight the “hidden” initial period of the epidemic (backward prediction). Namely, we have been able in dating back the beginning of epidemics some months before the first ascertained case. This occurrence, that recently has been acknowledge by new investigations12, tells about an ‘hidden circulation’ of the virus in Lombardia long ago before any official evidence that could be one of the concurring causes of Lombardia singularity. On a more methodological ground it is worth noting how the sigmoidal model was able to correctly estimate the time course of the derivative of epidemic spread (the same information conveyed by SEIR-based R-like statistics) .when fed of only early (and very uncertain) data before 24 March 2020 (Figure 4).