A deterministic compartmental model for the transition between variants in the spread of Covid-19 in Italy.

We propose a deterministic epidemic model to describe the transition between two variants of the same virus, through the combination of a series of realistic mechanisms such as partial cross immunity, waning immunity for vaccinated individuals and a novel data-based algorithm to describe the average immunological status of the population. The model is validated on the evolution of Covid-19 in Italy, during the period in which the transition between Delta and Omicron variant occurred, with very satisfactory agreement with the experimental data. According to our model, if the vaccine efficacy had been equal against Delta and Omicron variant infections, the transition would have been smoothed and the epidemic would have gone extinct. This circumstance confirms the fundamental role of vaccines in combating the epidemic, and the importance of identifying vaccines capable of intercepting new variants.

Vaccination and variants: Retrospective model for the evolution of Covid-19 in Italy.

The last year of Covid-19 pandemic has been characterized by the continuous chase between the vaccination campaign and the appearance of new variants that puts further obstacles to the possibility of eradicating the virus and returning to normality in a short period. In the present paper we develop a deterministic compartmental model to describe the evolution of the Covid-19 in Italy as a combined effect of vaccination campaign, new variant spreading and mobility restrictions. Particular attention is given to the mechanism of waning immunity, appropriately timed with respect to the effective progress of the vaccination campaign in Italy. We perform a retrospective analysis in order to explore the role that different mechanisms, such as behavioral changes, variation of the population mobility, seasonal variability of the virus infectivity, and spreading of new variants have had in shaping the epidemiological curve. We find that, in the large time window considered, the most relevant mechanism is the seasonal variation in the stability of the virus, followed by the awareness mechanism, that induces individuals to increase/relax self-protective measures when the number of active cases increases/decreases. The appearance of the Delta variant and the mobility variations have had instead only marginal effects. In absence of vaccines the emerging scenario would have been dramatic with a percentage difference in the number of total infections and total deaths, in both cases, larger than fifty per cent. The model also predicts the appearance of a more contagious variant (the Omicron variant) and its becoming dominant in January 2022.

Beyond the peak: A deterministic compartment model for exploring the Covid-19 evolution in Italy.

Novel Covid-19 has had a huge impact on the world's population since December 2019. The very rapid spreading of the virus worldwide, with its heavy toll of death and overload of the healthcare systems, induced the scientific community to focus on understanding, monitoring and foreseeing the epidemic evolution, weighing up the impact of different containment measures. An immense literature was produced in few months. Many papers were focused on predicting the peak features through a variety of different models. In the present paper, combining the surveillance data-set with data on mobility and testing, we develop a deterministic compartment model aimed at performing a retrospective analysis to understand the main modifications occurred to the characteristic parameters that regulate the epidemic spreading. We find that, besides self-protective behaviors, a reduction of susceptibility should have occurred in order to explain the fast descent of the epidemic after the peak. A sensitivity analysis of the basic reproduction number, in response to variations of the epidemiological parameters that can be influenced by policy-makers, shows the primary importance of a rigid isolation procedure for the diagnosed cases, combined with an intensive effort in performing extended testing campaigns. Future scenarios depend on the ability to protect the population from the injection of new cases from abroad, and to pursue in applying rigid self-protective measures.

Modeling DNA Methylation Profiles through a Dynamic Equilibrium between Methylation and Demethylation.

DNA methylation is a heritable epigenetic mark that plays a key role in regulating gene expression. Mathematical modeling has been extensively applied to unravel the regulatory mechanisms of this process. In this study, we aimed to investigate DNA methylation by performing a high-depth analysis of particular loci, and by subsequent modeling of the experimental results. In particular, we performed an in-deep DNA methylation profiling of two genomic loci surrounding the transcription start site of the D-Aspartate Oxidase and the D-Serine Oxidase genes in different samples (n = 51). We found evidence of cell-to-cell differences in DNA methylation status. However, these cell differences were maintained between different individuals, which indeed showed very similar DNA methylation profiles. Therefore, we hypothesized that the observed pattern of DNA methylation was the result of a dynamic balance between DNA methylation and demethylation, and that this balance was identical between individuals. We hence developed a simple mathematical model to test this hypothesis. Our model reliably captured the characteristics of the experimental data, suggesting that DNA methylation and demethylation work together in determining the methylation state of a locus. Furthermore, our model suggested that the methylation status of neighboring cytosines plays an important role in this balance.

Relation between statics and dynamics in the quench of the Ising model to below the critical point.

The standard phase-ordering process is obtained by quenching a system, like the Ising model, to below the critical point. This is usually done with periodic boundary conditions to ensure ergodicity breaking in the low-temperature phase. With this arrangement the infinite system is known to remain permanently out of equilibrium, i.e., there exists a well-defined asymptotic state which is time invariant but different from the ordered ferromagnetic state. In this paper we establish the critical nature of this invariant state by demonstrating numerically that the quench dynamics with periodic and antiperiodic boundary conditions are indistinguishable from each other. However, while the asymptotic state does not coincide with the equilibrium state for the periodic case, it coincides instead with the equilibrium state of the antiperiodic case, which in fact is critical. The specific example of the Ising model is shown to be one instance of a more general phenomenon, since an analogous picture emerges in the spherical model, where boundary conditions are kept fixed to periodic, while the breaking or preserving of ergodicity is managed by imposing the spherical constraint either sharply or smoothly.

A biological control model to manage the vector and the infection of Xylella fastidiosa on olive trees.

Xylella fastidiosa pauca ST53 is the bacterium responsible for the Olive Quick Decline Syndrome that has killed millions of olive trees in Southern Italy. A recent work demonstrates that a rational integration of vector and transmission control measures, into a strategy based on chemical and physical control means, can manage Xylella fastidiosa invasion and impact below an acceptable economic threshold. In the present study, we propose a biological alternative to the chemical control action, which involves the predetermined use of an available natural enemy of Philaenus spumarius, i.e., Zelus renardii, for adult vector population and infection biocontrol. The paper combines two different approaches: a laboratory experiment to test the predation dynamics of Zelus renardii on Philaenus spumarius and its attitude as candidate for an inundation strategy; a simulated experiment of inundation, to preliminary test the efficacy of such strategy, before eventually proceeding to an in-field experimentation. With this double-fold approach we show that an inundation strategy with Zelus renardii has the potential to furnish an efficient and "green" solution to Xylella fastidiosa invasion, with a reduction of the pathogen incidence below 10%. The biocontrol model presented here could be promising for containing the impact and spread of Xylella fastidiosa, after an in-field validation of the inundation technique. Saving the fruit orchard, the production and the industry in susceptible areas could thus become an attainable goal, within comfortable parameters for sustainability, environmental safety, and effective plant health protection in organic orchard management.

Nucleotide distance influences co-methylation between nearby CpG sites.

The tendency of individual CpG sites to be methylated is distinctive, non-random and well-regulated throughout the genome. We investigated the structural and spatial factors influencing CpGs methylation by performing an ultra-deep targeted methylation analysis on human, mouse and zebrafish genes. We found that methylation is not a random process and that closer neighboring CpG sites are more likely to share the same methylation status. Moreover, if the distance between CpGs increases, the degree of co-methylation decreases. We set up a simulation model to analyze the contribution of both the intrinsic susceptibility and the distance effect on the probability of a CpG to be methylated. Our finding suggests that the establishment of a specific methylation pattern follows a universal rule that must take into account of the synergistic and dynamic interplay of these two main factors: the intrinsic methylation susceptibility of specific CpG and the nucleotide distance between two CpG sites.

A lattice model to manage the vector and the infection of the Xylella fastidiosa on olive trees.

Since October 2013 a new devastating plant disease, known as Olive Quick Decline Syndrome, has been killing most of the olive trees distributed in Apulia, South Italy. Xylella fastidiosa pauca ST53 is the plant pathogenic bacterium responsible for the disease, and the adult Meadow Spittlebug, Philaenus spumarius (L.) (Hemiptera Aphrophoridae), is its main vector. This study proposes a lattice model for the pathogen invasion of olive orchard aimed at identifying an appropriate strategy for arresting the infection, built on the management of the vector throughout its entire life cycle. In our model the olive orchard is depicted as a simple square lattice with olive trees and herbaceous vegetation distributed on the lattice sites in order to mimic the typical structure of an olive orchard; adult vectors are represented by particles moving on the lattice according to rules dictated by the interplay between vector and vegetation life cycles or phenology; the transmission process of the bacterium is regulated by a stochastic Susceptible, Infected and Removed model. On this baseline model, we build-up a proper Integrated Pest Management strategy based on tailoring, timing, and tuning of available control actions. We demonstrate that it is possible to reverse the hitherto unstoppable Xylella fastidiosa pauca ST53 invasion, by a rational vector and transmission control strategy.

Condensation of fluctuations in the Ising model: A transition without spontaneous symmetry breaking.

The ferromagnetic transition in the Ising model is the paradigmatic example of ergodicity breaking accompanied by symmetry breaking. It is routinely assumed that the thermodynamic limit is taken with free or periodic boundary conditions. More exotic symmetry-preserving boundary conditions, like cylindrical antiperiodic, are less frequently used for special tasks, such as the study of phase coexistence or the roughening of an interface. Here we show, instead, that when the thermodynamic limit is taken with these boundary conditions, a novel type of transition takes place below T_{c} (the usual Ising transition temperature) without breaking either ergodicity or symmetry. Then the low-temperature phase is characterized by a regime (condensation) of strong magnetization's fluctuations which replaces the usual ferromagnetic ordering. This is due to critical correlations perduring for all T below T_{c}. The argument is developed exactly in the d=1 case and numerically in the d=2 case.

Simple and Flexible Model for Laser-Driven Antibody-Gold Surface Interactions: Functionalization and Sensing.

Interactions between biomolecules and between substrates and biomolecules is a crucial issue in physics and applications to topics such as biotechnology and organic electronics. The efficiency of bio- and mechanical sensors, of organic electronics systems, and of a number of other devices critically depends on how molecules are deposited on a surface so that these acquire specific functions. Here, we tackle this vast problem by developing a coarse grained model of biomolecules having a recognition function, such as antibodies, capable to quantitatively describe in a simple manner essential phenomena: antigen-antibody and antibody substrate interactions. The model is experimentally tested to reproduce the results of a benchmark case, such as (1) gold surface functionalization with antibodies and (2) antibody-antigen immune-recognition function. The agreement between experiments and model prediction is excellent, thus unveiling the mechanism for antibody immobilization onto metals at the nanoscale in various functionalization schemes. These results shed light on the geometrical packing properties of the deposited molecules, and may open the way to a novel coarse-grained based approach to describe other processes where molecular packing is a key issue with applications in a huge number of fields from nano- to biosciences.

Scaling and universality in glass transition.

Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are within those systems known to exhibit a discontinuous dynamical transition with a two step relaxation. We consider a general scaling approach, within mean field theory, for such systems by considering the behavior of the density correlator 〈q(t)〉 and the dynamical susceptibility 〈q(2)(t)〉 - 〈q(t)〉(2). Focusing on the Fredrickson and Andersen (FA) facilitated spin model on the Bethe lattice, we extend a cluster approach that was previously developed for continuous glass transitions by Arenzon et al. (Phys. Rev. E 90, 020301(R) (2014)) to describe the decay to the plateau, and consider a damage spreading mechanism to describe the departure from the plateau. We predict scaling laws, which relate dynamical exponents to the static exponents of mean field bootstrap percolation. The dynamical behavior and the scaling laws for both density correlator and dynamical susceptibility coincide with those predicted by MCT. These results explain the origin of scaling laws and the universal behavior associated with the glass transition in mean field, which is characterized by the divergence of the static length of the bootstrap percolation model with an upper critical dimension dc = 8.

Multiple Lattice Model for Influenza Spreading.

Behavioral differences among age classes, together with the natural tendency of individuals to prefer contacts with individuals of similar age, naturally point to the existence of a community structure in the population network, in which each community can be identified with a different age class. Data on age-dependent contact patterns also reveal how relevant is the role of the population age structure in shaping the spreading of an infectious disease. In the present paper we propose a simple model for epidemic spreading, in which a contact network with an intrinsic community structure is coupled with a simple stochastic SIR model for the epidemic spreading. The population is divided in 4 different age-communities and hosted on a multiple lattice, each community occupying a specific age-lattice. Individuals are allowed to move freely to nearest neighbor empty sites on the age-lattice. Different communities are connected with each other by means of inter-lattices edges, with a different number of external links connecting different age class populations. The parameters of the contact network model are fixed by requiring the simulated data to fully reproduce the contact patterns matrices of the Polymod survey. The paper shows that adopting a topology which better implements the age-class community structure of the population, one gets a better agreement between experimental contact patterns and simulated data, and this also improves the accordance between simulated and experimental data on the epidemic spreading.

Percolation approach to glassy dynamics with continuously broken ergodicity.

We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At the mean-field level this approach is consistent with the mode-coupling theory (MCT) of type-A liquid-glass transitions and allows one to disentangle the universal and nonuniversal contributions to MCT relaxation exponents. Scaling predictions for the time correlation function are successfully tested in the F(12) schematic model and facilitated spin systems on a Bethe lattice. Our approach immediately suggests the extension of MCT scaling laws to finite spatial dimensions and yields predictions for dynamic relaxation exponents below an upper critical dimension of 6.

Dynamical arrest: interplay of glass and gel transitions.

The structural arrest of a polymeric suspension might be driven by an increase of the cross-linker concentration, which drives the gel transition, as well as by an increase of the polymer density, which induces a glass transition. These dynamical continuous (gel) and discontinuous (glass) transitions might interfere, since the glass transition might occur within the gel phase, and the gel transition might be induced in a polymer suspension with glassy features. Here we study the interplay of these transitions by investigating via event-driven molecular dynamics simulation the relaxation dynamics of a polymeric suspension as a function of the cross-linker concentration and the monomer volume fraction. We show that the slow dynamics within the gel phase is characterized by a long sub-diffusive regime, which is due both to the crowding as well as to the presence of a percolating cluster. In this regime, the transition of structural arrest is found to occur either along the gel or along the glass line, depending on the length scale at which the dynamics is probed. Where the two lines meet there is no apparent sign of higher order dynamical singularity. Logarithmic behavior typical of A3 singularity appears inside the gel phase along the glass transition line. These findings seem to be related to the results of the mode coupling theory for the F13 schematic model.

Lattice model for influenza spreading with spontaneous behavioral changes.

Individual behavioral response to the spreading of an epidemic plays a crucial role in the progression of the epidemic itself. The risk perception induces individuals to adopt a protective behavior, as for instance reducing their social contacts, adopting more restrictive hygienic measures or undergoing prophylaxis procedures. In this paper, starting with a previously developed lattice-gas SIR model, we construct a coupled behavior-disease model for influenza spreading with spontaneous behavioral changes. The focus is on self-initiated behavioral changes that alter the susceptibility to the disease, without altering the contact patterns among individuals. Three different mechanisms of awareness spreading are analyzed: the local spreading due to the presence in the neighborhood of infective individuals; the global spreading due to the news published by the mass media and to educational campaigns implemented at institutional level; the local spreading occurring through the "thought contagion" among aware and unaware individuals. The peculiarity of the present approach is that the awareness spreading model is calibrated on available data on awareness and concern of the population about the risk of contagion. In particular, the model is validated against the A(H1N1) epidemic outbreak in Italy during the 2009/2010 season, by making use of the awareness data gathered by the behavioral risk factor surveillance system (PASSI). We find that, increasing the accordance between the simulated awareness spreading and the PASSI data on risk perception, the agreement between simulated and experimental epidemiological data improves as well. Furthermore, we show that, within our model, the primary mechanism to reproduce a realistic evolution of the awareness during an epidemic, is the one due to globally available information. This result highlights how crucial is the role of mass media and educational campaigns in influencing the epidemic spreading of infectious diseases.

A lattice model for influenza spreading.

We construct a stochastic SIR model for influenza spreading on a D-dimensional lattice, which represents the dynamic contact network of individuals. An age distributed population is placed on the lattice and moves on it. The displacement from a site to a nearest neighbor empty site, allows individuals to change the number and identities of their contacts. The dynamics on the lattice is governed by an attractive interaction between individuals belonging to the same age-class. The parameters, which regulate the pattern dynamics, are fixed fitting the data on the age-dependent daily contact numbers, furnished by the Polymod survey. A simple SIR transmission model with a nearest neighbors interaction and some very basic adaptive mobility restrictions complete the model. The model is validated against the age-distributed Italian epidemiological data for the influenza A(H1N1) during the [Formula: see text] season, with sensible predictions for the epidemiological parameters. For an appropriate topology of the lattice, we find that, whenever the accordance between the contact patterns of the model and the Polymod data is satisfactory, there is a good agreement between the numerical and the experimental epidemiological data. This result shows how rich is the information encoded in the average contact patterns of individuals, with respect to the analysis of the epidemic spreading of an infectious disease.

Relaxation process and dynamical heterogeneities in chemical gels: critical behavior of self-overlap and its fluctuation.

We study the dynamical behavior in chemical gelation, as the gelation threshold is approached from the sol phase. On the basis of the heterogeneous diffusion due to the cluster size distribution, as expected by the percolation theory, we predict the long time decay of the self-overlap as a power law in time t(-3/2). Moreover, under the hypothesis that the cluster diffusion coefficient decreases in size as a power law, s(-x), the fluctuation of the self-overlap, χ(4)(t), exhibits growth at short time as t((3-τ)/x), where τ is the cluster size distribution critical exponent. At longer times, χ(4)(t) decays as t(-3/2) while, at intermediate times, it reaches a maximum at time t*, which scales as s*(x), where s* is the size of the critical cluster. Finally, the value of the maximum χ(4)(t*) scales as the mean cluster size. The theoretical predictions are in agreement with molecular dynamic calculations in a model system, where spherical monomers are bonded by a finite extendable nonlinear elastic (FENE) potential.

Clusters in colloidal systems.

We study the dynamical properties of a model for charged colloidal particles, performing molecular dynamics simulations and observing the behavior of bond persistence functions, self-intermediate scattering functions at different wave vectors, and mean-square displacements of the particles, in three different regimes of the volume fraction. At the lowest volume fraction the system displays properties very similar to those of a gelling system, which can be interpreted in terms of the distribution of cluster sizes, with a peak in the dynamical susceptibility at the lowest wave vector. At the highest volume fraction, a percolating network of bonds is always present, and the system is strongly reminiscent of strong glasses, with the maximum in the dynamical susceptibility increasing when the temperature is lowered, and an Arrhenius dependence of the relaxation times. At intermediate volume fractions, a complex behavior is found, where both the distribution of cluster sizes and the intercluster correlations due to crowding are important.

Granular species segregation under vertical tapping: effects of size, density, friction, and shaking amplitude.

We present extensive molecular dynamics simulations on species segregation in a granular mixture subject to vertical taps. We discuss how grain properties, e.g., size, density, friction, as well as shaking properties, e.g., amplitude and frequency, affect such a phenomenon. Both the Brazil nut effect (larger particles on the top, BN) and the reverse Brazil nut effect (larger particles on the bottom, RBN) are found and we derive the system comprehensive "segregation diagram" and the BN to RBN crossover line. We also discuss the role of friction and show that particles which differ only for their frictional properties segregate in states depending on the tapping acceleration and frequency.

Segregation in fluidized versus tapped packs.

We compare the predictions of two different statistical mechanics approaches, corresponding to different physical measurements, proposed to describe binary granular mixtures subjected to some external driving (continuous shaking or tap dynamics). In particular we analytically solve at a mean field level the partition function of a simple hard sphere lattice model under gravity and focus on the phenomenon of size segregation. We find that the two approaches lead to similar results and seem to coincide in the limit of very low shaking amplitude. However, they give different predictions of the crossovers from Brazil nut effect to reverse Brazil nut effect with respect to the shaking amplitude, which could be detected experimentally.