Modeling and simulation of the infection zone from a cough
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ORIGINAL PAPER
Modeling and simulation of the infection zone from a cough T. I. Zohdi1 Received: 22 May 2020 / Accepted: 8 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The pandemic of 2020 has led to a huge interest of modeling and simulation of infectious diseases. One of the central questions is the potential infection zone produced by a cough. In this paper, mathematical models are developed to simulate the progressive time-evolution of the distribution of locations of particles produced by a cough. Analytical and numerical studies are undertaken. The models ascertain the range, distribution and settling time of the particles under the influence of gravity and drag from the surrounding air. Beyond qualitative trends that illustrate that large particles travel far and settle quickly, while small particles do not travel far and settle slowly, the models provide quantitative results for distances travelled and settling times, which are needed for constructing social distancing policies and workplace protocols. Keywords Pandemic · Cough · Infection · Particles · Spread · Simulation
1 Introduction The pandemic of 2020, due to SARS-CoV-2, named COVID19 and referred to as coronavirus, has been responsible for hundreds of thousands of deaths in 2020 alone. It is well-established that this virus primarily spreads from person-to-person contact by respiratory droplets produced when an infected person coughs or sneezes. Subsequently, the droplets come into contact with the eyes, nose or mouth of a nearby person or when a person touches an infected surface, then makes contact with their eyes, nose or mouth. Since the virus is small, 0.06–0.14 microns in diameter, it can be contained in or attached to such emitted droplets. Droplets as small as one micron can carry enough viral load to cause an infection. A particular concern is the interaction of droplets with ventilation systems, which potentially could enhance the propagation of pathogens. This has implications on situation-specific safe distancing and the design of building filtration systems, air distribution, heating, air-conditioning and decontamination systems, for example using UV-c and related technologies. In order to facilitate such system redesigns, fundamental analysis tools are needed that are easy to use. Accordingly, this paper develops one type
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T. I. Zohdi [email protected] Department of Mechanical Engineering, University of California, 6195 Etcheverry Hall, Berkeley, CA 94720-1740, USA
of such needed tools, namely a simulator for the analysis of cough particle tracking, in order to ascertain how large is the potential infection zone and the airborne setting time of cough particles. In its most basic form, a cough can be considered as a high-velocity release of a random distribution of particles of various sizes, into an ambient atmosphere. We refer the reader to Wei and Li [53], Duguid [11], Papineni and Rosenthal [37], Wei and Li [54], Zhu et al. [59], Chao et al. [9], Morawska et al. [31], VanSciver et al.
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