Statistical analysis of infectious disease transmission risk based on exhaled respiratory droplet trajectory distribution

Abstract

In the present work, the risk of infectious disease transmission is evaluated based on a statistical analysis of respiratory droplet trajectory distribution. An analytical model recently developed by the authors allows the prediction of the trajectory and evaporation rate of exhaled droplets. The model is used to collect data from a sampling set of more than twenty thousand droplets distributed over a range of diameters from 0.1 μm to 1 mm for different respiratory scenarios. The analytical tool implements the governing equations of droplet transport, evaporation, energy balance, and chemical composition. It also features a two-dimensional unsteady empirical model of respiratory cloud including momentum dissipation and buoyancy. A discrete random walk approach to simulate the droplet turbulent dispersion, and the randomization of the droplet release within the exhalation period and the mouth cross section area complete the model enabling statistical analyses to be rightly performed. With the due boundary conditions, different types of respiratory events can be modeled easily. With additional information on the exhaled droplet size distribution and viral content, spatial maps of virus concentration are derived and associated with the risk of infectious disease transmission being able to discriminate between various transmission routes such as fomite, airborne, or direct inhalation. Different scenarios are presented including mouth breathing, nose breathing, speaking, coughing, and sneezing. The fluid dynamic behavior of respiratory droplets is explored on a size basis, and the role of ventilation discussed. Risk evaluation provides useful information for a knowledgeable discussion on the prevention needs and means from case to case.