New Insights into the Estimation of Reproduction Numbers during an Epidemic.

In this paper, we deal with the problem of estimating the reproduction number Rt during an epidemic, as it represents one of the most used indicators to study and control this phenomenon. In particular, we focus on two issues. First, to estimate Rt, we consider the use of positive test case data as an alternative to the first symptoms data, which are typically used. We both theoretically and empirically study the relationship between the two approaches. Second, we modify a method for estimating Rt during an epidemic that is widely used by public institutions in several countries worldwide. Our procedure is not affected by the problems deriving from the hypothesis of Rt local constancy, which is assumed in the standard approach. We illustrate the results obtained by applying the proposed methodologies to real and simulated SARS-CoV-2 datasets. In both cases, we also apply some specific methods to reduce systematic and random errors affecting the data. Our results show that the Rt during an epidemic can be estimated by using the positive test data, and that our estimator outperforms the standard estimator that makes use of the first symptoms data. It is hoped that the techniques proposed here could help in the study and control of epidemics, particularly the current SARS-CoV-2 pandemic.

COVID-19 Pandemic: Influence of Schools, Age Groups, and Virus Variants in Italy.

The estimated smooth curve of the percentage of subjects positive to SARS-CoV-2 started decreasing in Italy at the beginning of January 2021, due to the government containment measures undertaken from Christmas until 7 January. Approximately two weeks after releasing the measures, the curve stopped to decrease and remained approximately constant for four weeks to increase again in the middle of February. This epidemic phase had a public health care impact since, from the beginning of the fourth week of February, the curve of the intensive care unit's occupancy started to grow. This wave of infection was characterized by the presence of new virus variants, with a higher than 80% dominance of the so-called "English" variant, since 15 April. School activities in Italy started at different times from 7 January until 8 February, depending on every region's decision. Our present data on the incidence of SARS-CoV-2 in different age groups in Italy are in agreement with literature reports showing that subjects older than 10 years are involved in virus transmission. More importantly, we provide evidence to support the hypothesis that also individuals of age 0-9 years can significantly contribute to the spread of SARS-CoV-2.

Spatiotemporal Analysis of COVID-19 Incidence Data.

(1) Background: A better understanding of COVID-19 dynamics in terms of interactions among individuals would be of paramount importance to increase the effectiveness of containment measures. Despite this, the research lacks spatiotemporal statistical and mathematical analysis based on large datasets. We describe a novel methodology to extract useful spatiotemporal information from COVID-19 pandemic data. (2) Methods: We perform specific analyses based on mathematical and statistical tools, like mathematical morphology, hierarchical clustering, parametric data modeling and non-parametric statistics. These analyses are here applied to the large dataset consisting of about 19,000 COVID-19 patients in the Veneto region (Italy) during the entire Italian national lockdown. (3) Results: We estimate the COVID-19 cumulative incidence spatial distribution, significantly reducing image noise. We identify four clusters of connected provinces based on the temporal evolution of the incidence. Surprisingly, while one cluster consists of three neighboring provinces, another one contains two provinces more than 210 km apart by highway. The survival function of the local spatial incidence values is modeled here by a tapered Pareto model, also used in other applied fields like seismology and economy in connection to networks. Model's parameters could be relevant to describe quantitatively the epidemic. (4) Conclusion: The proposed methodology can be applied to a general situation, potentially helping to adopt strategic decisions such as the restriction of mobility and gatherings.

Vaccination Criteria Based on Factors Influencing COVID-19 Diffusion and Mortality.

SARS-CoV-2 is highly contagious, rapidly turned into a pandemic, and is causing a relevant number of critical to severe life-threatening COVID-19 patients. However, robust statistical studies of a large cohort of patients, potentially useful to implement a vaccination campaign, are rare. We analyzed public data of about 19,000 patients for the period 28 February to 15 May 2020 by several mathematical methods. Precisely, we describe the COVID-19 evolution of a number of variables that include age, gender, patient's care location, and comorbidities. It prompts consideration of special preventive and therapeutic measures for subjects more prone to developing life-threatening conditions while affording quantitative parameters for predicting the effects of an outburst of the pandemic on public health structures and facilities adopted in response. We propose a mathematical way to use these results as a powerful tool to face the pandemic and implement a mass vaccination campaign. This is done by means of priority criteria based on the influence of the considered variables on the probability of both death and infection.

COVID-19 and School Activities in Italy.

After a linear growth during September, the diffusion in Italy of SARS-CoV-2, responsible for COVID-19, has been growing exponentially since the end of that month with a doubling time approximately equal to one week [...].

Covid-19 epidemic in Italy: evolution, projections and impact of government measures.

We report on the Covid-19 epidemic in Italy in relation to the extraordinary measures implemented by the Italian Government between the 24th of February and the 12th of March. We analysed the Covid-19 cumulative incidence (CI) using data from the 1st to the 31st of March. We estimated that in Lombardy, the worst hit region in Italy, the observed Covid-19 CI diverged towards values lower than the ones expected in the absence of government measures approximately 7-10 days after the measures implementation. The Covid-19 CI growth rate peaked in Lombardy the 22nd of March and in other regions between the 24th and the 27th of March. The CI growth rate peaked in 87 out of 107 Italian provinces on average 13.6 days after the measures implementation. We projected that the CI growth rate in Lombardy should substantially slow by mid-May 2020. Other regions should follow a similar pattern. Our projections assume that the government measures will remain in place during this period. The evolution of the epidemic in different Italian regions suggests that the earlier the measures were taken in relation to the stage of the epidemic, the lower the total cumulative incidence achieved during this epidemic wave. Our analyses suggest that the government measures slowed and eventually reduced the Covid-19 CI growth where the epidemic had already reached high levels by mid-March (Lombardy, Emilia-Romagna and Veneto) and prevented the rise of the epidemic in regions of central and southern Italy where the epidemic was at an earlier stage in mid-March to reach the high levels already present in northern regions. As several governments indicate that their aim is to "push down" the epidemic curve, the evolution of the epidemic in Italy supports the WHO recommendation that strict containment measures should be introduced as early as possible in the epidemic curve.

Magnitude-dependent epidemic-type aftershock sequences model for earthquakes.

We propose a version of the pure temporal epidemic type aftershock sequences (ETAS) model: the ETAS model with correlated magnitudes. As for the standard case, we assume the Gutenberg-Richter law to be the probability density for the magnitudes of the background events. Instead, the magnitude of the triggered shocks is assumed to be probabilistically dependent on that of the relative mother events. This probabilistic dependence is motivated by some recent works in the literature and by the results of a statistical analysis made on some seismic catalogs [Spassiani and Sebastiani, J. Geophys. Res. 121, 903 (2016)10.1002/2015JB012398]. On the basis of the experimental evidences obtained in the latter paper for the real catalogs, we theoretically derive the probability density function for the magnitudes of the triggered shocks proposed in Spassiani and Sebastiani and there used for the analysis of two simulated catalogs. To this aim, we impose a fundamental condition: averaging over all the magnitudes of the mother events, we must obtain again the Gutenberg-Richter law. This ensures the validity of this law at any event's generation when ignoring past seismicity. The ETAS model with correlated magnitudes is then theoretically analyzed here. In particular, we use the tool of the probability generating function and the Palm theory, in order to derive an approximation of the probability of zero events in a small time interval and to interpret the results in terms of the interevent time between consecutive shocks, the latter being a very useful random variable in the assessment of seismic hazard.

Evidences in favour of a single electron transfer (SET) mechanism in the TiO2 sensitized photo-oxidation of α-hydroxy- and α,ß-dihydroxybenzyl derivatives in water.

The TiO(2) photosensitized oxidation in water of a series of X-ring substituted benzyl alcohols gives the corresponding benzaldehyde. Kinetic evidence (from competitive experiments) suggests a single electron transfer (SET) mechanism with a changeover of the electron abstraction site from the aromatic moiety (X=4-OCH(3), 4-CH(3), H and 3-Cl) to the hydroxylic group (X=3-CF(3) and 4-CF(3)), probably due to the preferential adsorption of the above OH group on the TiO(2) surface. The same photo-oxidation of a series of 1-(X-phenyl)-1,2-ethanediols and of 2-(X-phenyl)-1,2-propanediols gives the corresponding benzaldehyde and acetophenone, respectively, accompanied by formaldehyde, whereas a series of symmetrically X-ring-substituted 1,2-diphenyl-1,2-ethanediols yields the corresponding benzaldehyde (substrate/product molar ratio=0.5). The relative rate values suggest a SET mechanism in all of the series, with electron abstraction from one of the two OH groups of all the considered diols, probably due to the much higher adsorption of the above groups (due to the chelation effect) on the semiconductor. Further confirmation of this mechanistic behaviour has been obtained from laser flash photolysis experiments.