Beyond well-mixed: A simple probabilistic model of airborne disease transmission in indoor spaces

We develop a simple model for assessing risk of airborne disease transmission that accounts for non-uniform mixing in indoor spaces and is compatible with existing epidemiological models. A database containing 174 high-resolution simulations of airflow in classrooms, lecture halls, and buses is generated and used to quantify the spatial distribution of expiratory droplet nuclei for a wide range of ventilation rates, exposure times, and room configurations. Imperfect mixing due to obstructions, buoyancy, and turbulent dispersion results in concentration fields with significant variance. The spatial non-uniformity is found to be accurately described by a shifted lognormal distribution. A well-mixed mass balance model is used to predict the mean, and the standard deviation is parameterized based on ventilation rate and room geometry. When employed in a dose-response function risk model, infection probability can be estimated considering spatial heterogeneity that contributes to both short- and long-range transmission.