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Gabriel Fabricius

Publications and source records attributed to Gabriel Fabricius.

7 recordsLinked to original sources

Epidemic spread: limiting contacts to regular circles is not necessarily the safest option

When a new infectious disease (or a new strain of an existing one) emerges, as in the recent COVID-19 pandemic, different types of mobility restrictions are considered to slow down or mitigate the spread of the disease. The measures to be adopted require carefully weighing the social cost against their impact on disease control. In this work, we analyze, in a context of mobility restrictions, the role of frequent versus occasional contacts in epidemic spread. We develop an individual-based mathematical model where frequent contacts among individuals (at home, work, schools) and occasional contacts (at stores, transport, etc.) are considered. We define several contact structures by varying the relative weight of frequent and occasional contacts while keeping the same initial growth rate of the epidemic. We find the remarkable result that the more frequent contacts prevail over occasional ones, the higher the epidemic peak, the sooner it occurs, and the greater the final number of individuals affected by the epidemic. We conduct our study using an SIR model, considering both exponential and deterministic recovery from infection, and obtain that this effect is more pronounced under deterministic recovery. We find that the impact of relaxation measures depends on the relative importance of frequent and occasional contacts within the considered social structures. Finally, we assess in which of the considered scenarios the homogeneous mixing approximation provides a reasonable description of the epidemic dynamics.

physics.soc-ph

Exploring the threshold of epidemic spreading for a stochastic SIR model with local and global contacts

The spread of an epidemic process is considered in the context of a spatial SIR stochastic model that includes a parameter $0\le p\le 1$ that assigns weights $p$ and $1- p$ to global and local infective contacts respectively. The model was previously studied by other authors in different contexts. In this work we characterized the behavior of the system around the threshold for epidemic spreading. We first used a deterministic approximation of the stochastic model and checked the existence of a threshold value of $p$ for exponential epidemic spread. An analytical expression, which defines a function of the quotient $α$ between the transmission and recovery rates, is obtained to approximate this threshold. We then performed different analyses based on intensive stochastic simulations and found that this expression is also a good estimate for a similar threshold value of $p$ obtained in the stochastic model. The dynamics of the average number of infected individuals and the average size of outbreaks show a behavior across the threshold that is well described by the deterministic approximation. The distributions of the outbreak sizes at the threshold present common features for all the cases considered corresponding to different values of $α>1$. These features are otherwise already known to hold for the standard stochastic SIR model at its threshold, $α=1$: (i) the probability of having an outbreak of size $n$ goes asymptotically as $n^{-3/2}$ for an infinite system, (ii) the maximal size of an outbreak scales as $N^{2/3}$ for a finite system of size $N$.

q-bio.PE

SIR model with local and global infective contacts: A deterministic approach and applications

An epidemic model with births and deaths is considered on a two dimensional LxL lattice. Each individual can have global infective contacts according to the standard SIR model rules or local infective contacts with its nearest neighbors. We propose a deterministic approach to this model and verified that there is a good agreement with the stochastic simulations for different situations of the disease transmission and parameters corresponding to pertussis and rubella in the prevaccine era.

q-bio.PE

SIR model on a dynamical network and the endemic state of an infectious disease

In this work we performed a numerical study of an epidemic model that mimics the endemic state of whooping cough in the pre-vaccine era. We considered a stochastic SIR model on dynamical networks that involve local and global contacts among individuals and analyzed the influence of the network properties on the characterization of the quasi-stationary state. We computed probability density functions (PDF) for infected fraction of individuals and found that they are well fitted by gamma functions, excepted the tails of the distributions that are q-exponentials. We also computed the fluctuation power spectra of infective time series for different networks. We found that network effects can be partially absorbed by rescaling the rate of infective contacts of the model. An explicit relation between the effective transmission rate of the disease and the correlation of susceptible individuals with their infective nearest neighbours was obtained. This relation quantifies the known screening of infective individuals observed in these networks. We finally discuss the goodness and limitations of the SIR model with homogeneous mixing and parameters taken from epidemiological data to describe the dynamic behaviour observed in the networks studied.

physics.soc-ph

From particles to spins: Eulerian formulation of supercooled liquids and glasses

The dynamics of supercooled liquid and glassy systems are usually studied within the Lagrangian representation, in which the positions and velocities of distinguishable interacting particles are followed. Within this representation, however, it is difficult to define measures of spatial heterogeneities in the dynamics, as particles move in and out of any one given region within long enough times. It is also non-transparent how to make connections between the structural glass and the spin glass problems within the Lagrangian formulation. We propose an Eulerian formulation of supercooled liquids and glasses that allows for a simple connection between particle and spin systems, and that permits the study of dynamical heterogeneities within a fixed frame of reference similar to the one used for spin glasses. We apply this framework to the study of the dynamics of colloidal particle suspensions for packing fractions corresponding to the supercooled and glassy regimes, which are probed via confocal microscopy.

cond-mat.dis-nn

Time correlation functions between Inherent Structures: a connection between landscape topology and the dynamics of glassy systems

We introduce time correlation functions between Inherent Structures (IS) of a supercooled liquid. We show that these functions are useful to relate the slowing down of the dynamics to the structure of the energy landscape near the glass transition temperature. They show a short time regime during which the system remains in the basin of a particular IS and a long time regime where it explores the neighborhood of an IS. We compare the behavior of these functions in a binary Lennard-Jones supercooled liquid and in a model of traps and show that they behave qualitatively different. This comparison reflects the presence/absence of structure in the landscape of the Lennard-Jones/traps models. Possible scenarios for the structure of the landscape which are compatible with these results are discussed.

cond-mat.dis-nn

The distance between Inherent Structures and the influence of saddles on approaching the mode coupling transition in a simple glass former

We analyze through molecular dynamics simulations of a Lennard-Jones binary mixture the statistics of the distances between inherent structures (IS) sampled at temperatures above the mode coupling transition temperature T_MCT. We take equilibrated configurations and randomly perturb the coordinates of a given number of particles. After that we take the nearest IS of both the original configuration and the perturbed one and evaluate the distance between them. This distance presents an inflection point near T~1 with a strong decrease below this temperature and goes to a small but nonzero value on approaching T_MCT. In the low temperature region we study the statistics of events which give zero distance, i.e. dominated by minima, and find evidence that the number of saddles decreases exponentially near T_MCT. This implies that saddles continue to exist even for T<=T_MCT. As at T_MCT the extrapolated diffusivity goes to zero our results imply that there are saddles associated with nondiffusional events at T<T_MCT.

cond-mat.dis-nn