COVID-19 Transmission by Small Droplets

Recent progress in the statistical theory of Lagrangian flow is used to study the distributions of passive scalars. The results are applied to the distribution of the small droplet transmission of the Coronavirus responsible for the Covid-19 pandemic. We compute the distribution of small droplets over 5 micrometers in diameter and simulate its evolution. The resulting distribution is used to compute the concentration of small droplet in a well-documented outbreak in a restaurant in Guangzhou China, see Lu, J. et al. Emerging Infectious Diseases, 26 (7) 2020. The simulations show that although some of the infected people may have been infected by confined clouds of droplets within one minute, a more likely source of the infection is a cloud of droplets, with increasing concentration in time, that engulfed the three tables where the infected people sat. The concentration of this cloud increased to a concentration ten times that of initial concentration during the hour that the three groups spent together in the restaurant. This example provides a stern warning against groups of people spending an extended time interval in confined spaces. The method can be used to study the spread of droplets in a wide variety of settings.