Modeling the viral load expelled in saliva droplets carrying SARS-CoV-2

Abstract

One of the most likely routes of transmission of COVID-19 is through the saliva droplets that are produced while speaking, coughing or sneezing by infected people. The expelled droplets, measuring between 0.4 and 450 μm, follow trajectories determined, mainly, by the gravitational, and air frictional forces. We solve numerically the equations of motion in which the linear and quadratic velocity terms in the drag force are considered. In order to model the virus load expelled during respiratory events, we assume log-log Gaussian distributions, with peaks around 10 μm, and analyze four size ranges: the aerosol (0.4-5 μm), the small (5.1-10 μm), the middle (10.1-100 μm), and big (100.1-450 μm) droplet size regimes. In the aerosol regime, the frictional forces quickly stop the droplets in their horizontal movement and they fall extremely slowly pulled down by the gravitational force. The residence time, in a calm environment, goes from 3.83 days to 33.3 min. More massive droplets take shorter times and hit the ground meters away from the source. By assuming a constant density of virions per milliliter, we estimate the expelled amount into the environment. The middle and small size droplets contain the highest amount but since the aerosol droplets remain in the air such a long time, they represent also a high risk for infection. We emphasize the importance of face protection to minimize COVID-19, transmission.