From microscopic droplets to macroscopic crowds: Crossing the scales in models of short-range respiratory disease transmission, with application to COVID-19

Abstract

Short-range exposure to airborne virus-laden respiratory droplets is now acknowledged as an effective transmission route of respiratory diseases, as exemplified by COVID-19. In order to assess the risks associated with this pathway in daily-life settings involving tens to hundreds of individuals, the chasm needs to be bridged between fluid dynamical simulations of droplet propagation and population-scale epidemiological models. We achieve this by coarse-graining microscopic droplet trajectories (simulated in various ambient flows) into spatio-temporal maps of viral concentration around the emitter and coupling these maps to field-data about pedestrian crowds in different scenarios (streets, train stations, markets, queues, and street caf{\'e}s). At the scale of an individual pedestrian, our results highlight the paramount importance of the velocity of the ambient air flow relative to the emitter's motion. This aerodynamic effect, which disperses infectious aerosols and thus mitigates short-range transmission risks, prevails over all other environmental variables. At the crowd's scale, the method yields a ranking of the scenarios by the risks of new infections that they present, dominated by the street caf{\'e}s and then the outdoor market. While the effect of light winds on the qualitative ranking is fairly marginal, even the most modest ambient air flows dramatically lower the quantitative rates of new infections. The proposed framework was here applied with SARS-CoV-2 in mind, but its generalization to other airborne pathogens and to other (real or hypothetical) crowd arrangements is straightforward.