Science News: Using Fluid Dynamics to Predict COVID transmission

    As the number of cases of COVID-19 beings to surge again, scientists are desperately working to find an effective cure and vaccine for the disease. In the meantime, people around the world continue to wear masks and maintain distance between each other as to slow the transmission of the virus. However, this is proving increasingly difficult for some people who question the effectiveness of masks in the first place. Scientists from John Hopkins University and University of Mississippi set out to answer these questions. These researchers developed a mathematical model that estimates the risk of transmission of the disease while wearing a mask based on basic fluid dynamics. The virus is spread when an infected individual releases aerosolized virus-containing droplets that survive in the air or on certain surfaces and then are able to enter the body of a second individual. There are a number of both concrete and abstract factors that contribute to viral transmission which researchers were eager to simplify.  That is when they discovered the Drake equation. The Drake equation was proposed in 1961 by Dr. Frank Drake to predict the number of extraterrestrial civilizations that may exist in our galaxy. Dr. Drake figured out that if he could quantify each variable that contributed to the likelihood of extraterrestrial life, he could multiple each factor together to create a probability of extraterrestrial life. Using this same approach, researchers created the contagion airborne transmission (CAT) inequality. By understanding the viral droplets as a fluid through the air, the researchers were able to use basic fluid dynamics to understand how different variables might impact transmission. The CAT is as follows:

where :

Ṙh	represents the rate of expulsion of respiratory droplets from the nose and mouth of the host (number of droplets per unit time),
fvh	represents the fractional viral emission load—the average number of virions contained in each expelled droplet,
fmh	represents the fraction of expelled droplets that make it past the face covering of the host,
fah	represents the fraction of expelled droplets that aerosolize (i.e., become suspended in the air),
fat	represents the fraction of aerosolized droplets that transport to the vicinity of the susceptible,
fvv	represents the fraction of aerosolized droplets transported to the vicinity of the susceptible that contain viable virions,
fis	represents the fraction of aerosols in the vicinity of the susceptible that would be inhaled by a susceptible not wearing a face covering,
fms	represents the fraction of inhaled aerosols that are filtered by the face covering of the susceptible,
Ṙtot	represents the total rate of viable virion inhalation by the susceptible (number per unit time),
Ts	represents the duration of exposure of the susceptible to the aerosols from the host, and
NID	represents the minimum number of inhaled virions required to initiate an infection in the susceptible.

The equation provides useful information about the spread of the virus. For example, if the distance between an infected person and a healthy person is doubled, the chance of infection is cut in half. Other factors, like physical exercise (which increases breathing rate) and using thin masks also increase the likelihood of transmission. While the model was designed specifically for COVID-19, it could be generalized to any virus transmitted in this way such as the flu. 

References:

Rajat Mittal et al, A mathematical framework for estimating risk of airborne transmission of COVID-19 with application to face mask use and social distancing, Physics of Fluids (2020). DOI: 10.1063/5.0025476

American Institute of Physics, Estimating risk of airborne COVID-19 with mask usage, social distancing, Physics.org (Oct 26, 2020) https://phys.org/news/2020-10-airborne-covid-mask-usage-social.html