Formulating Your Chances of Catching COVID-19

Winter 2021

Illustration of CAT inequality

In 1961, astronomer Frank Drake developed a simple equation—consisting of only seven variables—to estimate the probability of finding extraterrestrial civilizations in the Milky Way. Today, inspired by the Drake equation, fluid mechanics experts at the Whiting School of Engineering have developed a formula to answer the question of the moment: What determines someone’s chances of catching COVID-19?

In a paper published in Physics of Fluids, the researchers present a mathematical model to estimate the risk of airborne transmission of COVID-19. Insights from this new model could help assess how well preventive efforts, like mask wearing and social distancing, are protecting us in different transmission scenarios.

“There’s still much confusion about the transmission pathways of COVID-19. This is partly because there is no common ‘language’ that makes it easy to understand the risk factors involved,” says Rajat Mittal, coauthor of the paper and a professor in the Department of Mechanical Engineering.

“What really needs to happen for one to get infected? If we can visualize this process more clearly and in a quantitative manner, we can make better decisions about which activities to resume and which to avoid.”

What’s becoming clear is that COVID-19 is most commonly spread from person to person through the air, via small respiratory droplets generated by coughing, sneezing, talking, or breathing, according to a commentary published by 239 scientists in Clinical Infectious Diseases.

But the risk of getting infected with COVID-19 depends heavily on the circumstances, Mittal says. The team’s model considers 10 transmission variables, including the breathing rates of the infected and noninfected persons, the number of virus-carrying droplets expelled, the surrounding environment, and the exposure time. Multiplied together, these variables yield a calculation of the possibility that an individual will be infected with COVID-19.

The proposed formula is called the Contagion Airborne Transmission inequality.

“The CAT inequality is particularly useful because it translates the complex fluid dynamical transport process into a string of simple terms that is easy to understand,” says Charles Meneveau, the Louis M. Sardella Professor of Mechanical Engineering and coauthor of the study. “As we’ve seen, communicating science clearly is of paramount importance in public health and environmental crises like the one we are facing now.”

The team adds that the model can be useful to quantify the value of mask wearing and social distancing. If both people are wearing N95 masks, the risk of transmission is reduced by a factor of 400—that’s less than a 1% chance of getting the virus. But even a simple cloth mask will significantly reduce transmission probability, according to the model. The team also found that social distancing has a linear correlation to risk; if you double the distance, you double the protection factor, or reduce your risk by half.

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