Effect of manual and digital contact tracing on COVID-19 outbreaks: a study on empirical contact data.

Non-pharmaceutical interventions are crucial to mitigate the COVID-19 pandemic and contain re-emergence phenomena. Targeted measures such as case isolation and contact tracing can alleviate the societal cost of lock-downs by containing the spread where and when it occurs. To assess the relative and combined impact of manual contact tracing (MCT) and digital (app-based) contact tracing, we feed a compartmental model for COVID-19 with high-resolution datasets describing contacts between individuals in several contexts. We show that the benefit (epidemic size reduction) is generically linear in the fraction of contacts recalled during MCT and quadratic in the app adoption, with no threshold effect. The cost (number of quarantines) versus benefit curve has a characteristic parabolic shape, independent of the type of tracing, with a potentially high benefit and low cost if app adoption and MCT efficiency are high enough. Benefits are higher and the cost lower if the epidemic reproductive number is lower, showing the importance of combining tracing with additional mitigation measures. The observed phenomenology is qualitatively robust across datasets and parameters. We moreover obtain analytically similar results on simplified models.

Digital proximity tracing on empirical contact networks for pandemic control.

Digital contact tracing is a relevant tool to control infectious disease outbreaks, including the COVID-19 epidemic. Early work evaluating digital contact tracing omitted important features and heterogeneities of real-world contact patterns influencing contagion dynamics. We fill this gap with a modeling framework informed by empirical high-resolution contact data to analyze the impact of digital contact tracing in the COVID-19 pandemic. We investigate how well contact tracing apps, coupled with the quarantine of identified contacts, can mitigate the spread in real environments. We find that restrictive policies are more effective in containing the epidemic but come at the cost of unnecessary large-scale quarantines. Policy evaluation through their efficiency and cost results in optimized solutions which only consider contacts longer than 15-20 minutes and closer than 2-3 meters to be at risk. Our results show that isolation and tracing can help control re-emerging outbreaks when some conditions are met: (i) a reduction of the reproductive number through masks and physical distance; (ii) a low-delay isolation of infected individuals; (iii) a high compliance. Finally, we observe the inefficacy of a less privacy-preserving tracing involving second order contacts. Our results may inform digital contact tracing efforts currently being implemented across several countries worldwide.

Measuring contact patterns with wearable sensors: methods, data characteristics and applications to data-driven simulations of infectious diseases.

Thanks to recent technological advances, measuring real-world interactions by the use of mobile devices and wearable sensors has become possible, allowing researchers to gather data on human social interactions in a variety of contexts with high spatial and temporal resolution. Empirical data describing contact networks have thus acquired a high level of detail that may yield new insights into the dynamics of infection transmission between individuals. At the same time, such data bring forth new challenges related to their statistical description and analysis, and to their use in mathematical models. In particular, the integration of highly detailed empirical data in computational frameworks designed to model the spread of infectious diseases raises the issue of assessing which representations of the raw data work best to inform the models. There is an emerging need to strike a balance between simplicity and detail in order to ensure both generalizability and accuracy of predictions. Here, we review recent work on the collection and analysis of highly detailed data on temporal networks of face-to-face human proximity, carried out in the context of the SocioPatterns collaboration. We discuss the various levels of coarse-graining that can be used to represent the data in order to inform models of infectious disease transmission. We also discuss several limitations of the data and future avenues for data collection and modelling efforts in the field of infectious diseases.

[Periurethral pseudocysts following urethral injections of Zuidex: review of the literature]. / Pseudokystes periurétraux en complication des injections urétrales de Zuidex: revue de la littérature.

Periurethral dextranomer/hyaluronic acid (Zuidex) is a mini-invasive technique for female stress-urinary incontinence and minimal adverse effects were described. Pseudocysts were recently described. Twenty-nine cases only are reported in the literature and the authors illustrate the review with an additional case. Asymptomatic cases, pain and low stream were observed. On clinical examination, a tenderness or visible periurethral deformation need to precise the characteristics with ultrasonography and MRI. Symptomatic cases may benefit from puncture, although the patients must be informed of a potential recurrence of the incontinence.

Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction.

Combining analytical and numerical methods, we study within the framework of the homogeneous nonlinear Boltzmann equation a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism: namely, a deterministic nonlinear friction force. We derive analytically the high-energy tail of the velocity distribution and compare the theoretical predictions with high-precision numerical simulations. Stretched exponential forms are obtained when the nonequilibrium steady state is stable. We derive subleading corrections and emphasize their relevance. In marginal stability cases, power-law behaviors arise, with exponents obtained as the roots of transcendental equations. We also consider some simple Bhatnagar-Gross-Krook models, driven by similar heating devices, to test the robustness of our predictions.

The modeling of global epidemics: stochastic dynamics and predictability.

The global spread of emergent diseases is inevitably entangled with the structure of the population flows among different geographical regions. The airline transportation network in particular shrinks the geographical space by reducing travel time between the world's most populated areas and defines the main channels along which emergent diseases will spread. In this paper, we investigate the role of the large-scale properties of the airline transportation network in determining the global propagation pattern of emerging diseases. We put forward a stochastic computational framework for the modeling of the global spreading of infectious diseases that takes advantage of the complete International Air Transport Association 2002 database complemented with census population data. The model is analyzed by using for the first time an information theory approach that allows the quantitative characterization of the heterogeneity level and the predictability of the spreading pattern in presence of stochastic fluctuations. In particular we are able to assess the reliability of numerical forecast with respect to the intrinsic stochastic nature of the disease transmission and travel flows. The epidemic pattern predictability is quantitatively determined and traced back to the occurrence of epidemic pathways defining a backbone of dominant connections for the disease spreading. The presented results provide a general computational framework for the analysis of containment policies and risk forecast of global epidemic outbreaks.

The architecture of complex weighted networks.

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity. Along with a complex topological structure, real networks display a large heterogeneity in the capacity and intensity of the connections. These features, however, have mainly not been considered in past studies where links are usually represented as binary states, i.e., either present or absent. Here, we study the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively. In both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network. We define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices. This information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network. These results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks.

Observing brownian motion in vibration-fluidized granular matter.

Observation of the rotational brownian motion of a very fine wire immersed in a gas led to one of the most important ideas of equilibrium statistical mechanics. Namely, the many-particle problem of a large number of molecules colliding with the wire can be represented by just two macroscopic parameters: viscosity and temperature. Interest has arisen in the question of whether this idea (mathematically developed in the Langevin model and the fluctuation-dissipation theorem) can also be used to describe systems that are far from equilibrium. Here we report an experimental investigation of an archetypal non-equilibrium system, involving a sensitive torsion oscillator immersed in a granular system of millimetre-size grains that are fluidized by strong external vibrations. The vibro-fluidized granular medium is a driven environment, with continuous injection and dissipation of energy, and the immersed oscillator can be seen as analogous to an elastically bound brownian particle. By measuring the noise and the susceptibility, we show that the experiment can be treated (to a first approximation) with the equilibrium formalism. This gives experimental access to a granular viscosity and an effective temperature; however, these quantities are anisotropic and inhomogeneous. Surprisingly, the vibro-fluidized granular matter behaves as a 'thermal' bath satisfying a fluctuation-dissipation relation.

Random inelasticity and velocity fluctuations in a driven granular gas.

We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show that in its simplest version, the "stochastic thermostat" model of heated inelastic hard spheres, contrary to what has been hitherto stated, is incompatible with the experimental data, although predicting a reminiscent high-velocity stretched-exponential behavior with an exponent 3/2. The experimental observations lead to refine a recently proposed random restitution coefficient model. Very good agreement is then found with experimental velocity distributions within this framework, which appears self-consistent and further provides relevant probes to investigate the universality of the velocity statistics.

Real-space application of the mean-field description of spin-glass dynamics.

The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard "mean-field theory" versus "droplet picture" debate of the past decades. The main predictions of both theories concerning the spin-glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of a spin-glass coherence length, which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed.

Edwards' measures: a thermodynamic construction for dense granular media and glasses.

We present numerical support for the hypothesis that macroscopic observables of dense granular media and glasses can be evaluated from averages over typical blocked configurations: we construct the corresponding measure for a class of finite-dimensional systems and compare its predictions for various observables with the outcome of the out of equilibrium dynamics at large times. We discuss in detail the connection with the effective temperatures that appear in out of equilibrium glass theories, as well as the relation between our computation and those based on "inherent structure" arguments. A short version of this work has appeared in Phys. Rev. Lett. 85, 5034 (2000).

Edwards' measures for powders and glasses

Can one construct a thermodynamics for compact, slowly moving powders and grains? A few years ago, Edwards proposed a possible step in this direction, raising the fascinating perspective that such systems have a statistical mechanics of their own, different from that of Maxwell, Boltzmann, and Gibbs, allowing us to have some information while still ignoring dynamic details. Recent developments in the theory of glasses have come to confirm these ideas within mean field. In order to go beyond, we explicitly generate Edwards' measure in a 3D model. Comparison of the results with the irreversible compaction data shows very good agreement. The present framework immediately suggests new experimental checks.