A statistical analysis of exhaled respiratory droplet trajectory distribution in view of assessing the risk of infectious disease transmission

Abstract

In the present work an analytical model of exhaled droplet trajectory and evaporation is employed to perform a preliminary statistical analysis of the droplet spatial distribution. The analysis is carried out for a set of over twenty thousand droplets distributed in the range of diameters from 0.1 μm to 1 mm. The type of respiratory events modelled are mouth breathing and speaking. The analytical model employed has been recently developed by the authors. It implements the fundamental laws of fluid dynamics and convection-diffusion, and features a 2D empirical numerical model of buoyant intermittent jet modelling the exhaled breath cloud. A discrete random walk turbulent dispersion model is also included allowing statistical analysis of the droplet trajectory to be performed. With proper boundary conditions any type of respiratory event can be simulated making the model particularly versatile. From the analysis, spatial virus concentration maps are derived for the largest droplets falling to the ground, and for the smaller droplets remaining airborne in the area in front of an infected emitter and successively uniformly dispersed in the ambient. This allows to estimate the risk of infection by fomite, direct inhalation and indirect inhalation routes, and provide a better understanding of infectious disease transmission risks.