The reproduction number is broadly considered as a key indicator for the spreading of the COVID-19 pandemic. Its estimated value is a measure of the necessity and, eventually, effectiveness of interventions imposed in various countries. Here we present an online tool for the data-driven inference and quantification of uncertainties for the reproduction number, as well as the time points of interventions for 51 European countries. The study relied on the Bayesian calibration of the SIR model with data from reported daily infections from these countries. The model fitted the data, for most countries, without individual tuning of parameters. We also compared the results of SIR and SEIR models, which give different estimates of the reproduction number, and provided an analytical relationship between the respective numbers. We deployed a Bayesian inference framework with efficient sampling algorithms, to present a publicly available graphical user interface (https://cse-lab.ethz.ch/coronavirus) that allows the user to assess and compare predictions for pairs of European countries. The results quantified the rate of the disease's spread before and after interventions, and provided a metric for the effectiveness of non-pharmaceutical interventions in different countries. They also indicated how geographic proximity and the times of interventions affected the progression of the epidemic.

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We investigate the process of cloud cavitation collapse through large-scale simulation of a cloud composed of 12 500 gas bubbles. A finite volume scheme is used on a structured Cartesian grid to solve the Euler equations, and the bubbles are discretized by a diffuse interface method. We investigate the propagation of the collapse wave front through the cloud and provide comparisons to simplified models. We analyze the flow field to identify each bubble of the cloud and its associated microjet. We find that the oscillation frequency of the bubbles and the velocity magnitude of the microjets depend on the local strength of the collapse wave and hence on the radial position of the bubbles in the cloud. At the same time, the direction of the microjets is influenced by the distribution of the bubbles in its vicinity. Finally, an analysis of the pressure pulse spectrum shows that the pressure pulse rate is well captured by an exponential law. * petros@ethz.ch

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We present high-fidelity numerical simulations of expiratory biosol transport during normal breathing under indoor, stagnant air conditions with and without a facile mask. We investigate mask efficacy to suppress the spread of saliva particles that is underpinnings existing social distancing recommendations. The present simulations incorporate the effect of human anatomy and consider a spectrum of saliva particulate sizes that range from 0.1 to 10 μ m while also accounting for their evaporation. The simulations elucidate the vorticity dynamics of human breathing and show that without a facile mask, saliva particulates could travel over 2.2 m away from the person. However, a non-medical grade face mask can drastically reduce saliva particulate propagation to 0.72 m away from the person. This study provides new quantitative evidence that facile masks can successfully suppress the spreading of saliva particulates due to normal breathing in indoor environments.