# In Estimating COVID-19 Infection Risk, Frequency of an Activity Is Key

With proper precautions, the risk of a day at work, a ride on the bus, or a workout at the gym may be acceptable, write Yale SOM’s Arthur J. Swersey and his co-authors. But that risk compounds dramatically when an activity is repeated day after day.

- Arthur J. SwerseyProfessor Emeritus of Operations Research
- Johannes LedolterProfessor of Business Analytics and Statistics/Actuarial Science, University of Iowa
- Ellis Reid ’10Brand Strategy Consultant

As the economy reopens and people venture out more regularly, we are all looking for guidance on the risk of being infected with COVID-19 during day-to-day activities. An MIT study ranked the tradeoffs involved in going to various destinations, based on their usefulness and risk of infection. A *New York Times* op-ed used cell phone data to assess risks associated with different activities, based on how many people visit a location and how long they stay.

But these authors and others fail to consider that the risk of an individual activity is compounded by the frequency with which one undertakes it. The risk of a single instance of an activity may be low, but if done often enough, the risk of that activity may become unacceptable.

For example, two studies suggest that use of public transportation has contributed to the racial disparities in COVID-19 infection and death. It is not surprising that people have been infected riding public transportation to work, because each trip is risky, and many riders do it twice a day.

In order to demonstrate the importance of the frequency of an activity in calculating risk, our approach is to assume a probability for the risk of a single visit and then show how the probability of infection grows with increases in the number of visits. We illustrate the procedure and show results for two common activities, going to the gym and walking the dog.

Assume your chance of being infected on a single visit to the gym is one in one hundred (1%) or in the language of probability, 0.01, and the chance of not being infected is 0.99. This chance of being infected on a single visit will change over time, so think of that probability as the average over the period we are considering. Assume you go to the gym 4 times per week. What is the chance of being infected over the next 12 weeks, which entails 48 visits?

Assume the visits to the gym are independent—that is, the risk of one visit is not linked to the risk of another. As the number of visits increases, the chance of being infected increases and the chance of not being infected decreases. Applying the multiplication rule for independent events, the chance of *not* being infected is the probability of not being infected on the first visit (.99) times the probability of not being infected on the second visit (.99) times the probability of not being infected on the third visit (.99) and so forth. Performing the multiplication by 0.99 for 48 visits, which is 0.99 raised to the 48th power, we find that the probability of not being infected over 48 visits is 0.62 or 62%, meaning the probability of being infected is 38%—nearly a 40-fold increase compared to the risk of a single visit.

Our model is an approximation, because it ignores the possibility that you will stop the activity if you get infected and have symptoms. But the true probability of infection will only be slightly smaller than our estimate. If the virus is still around after 12 weeks, and you keep going to the gym, your risk will continue to increase.

But perhaps our original assumption is faulty. Perhaps increased distancing between users, wearing of masks for employees and customers, and frequent disinfecting of apparatus and equipment means that the risk of a single visit is 1 in 1,000 rather than 1 in 100. In that case, the risk of being infected over 48 visits would be reduced to 5%—still a sizeable risk.

Many activities are undertaken far more frequently than visits to the gym. Suppose you walk your dog three times a day in a populous area of a city. You take the elevator each time to exit the building and return to your apartment. We recognize that a single walk of the dog would be less risky than a visit to the gym, but as a starting point, assume your chance of being infected on one walk is 1 in 1,000 (0.001). Again, assume the walks are independent. Applying the same approach as above, the probability of being infected if you walk your dog three times a day for 90 days is about 25%! This is not acceptable. If instead the risk on each walk were 1 in 10,000, the chance of not being infected over 270 walks would be 0.97 or 97%, and the chance of being infected would be 3%. These results tell us that to be safe, the probability of being infected on each walk needs to be very low, because you walk the dog so often.

You can do similar calculations for other activities, such as shopping at a supermarket or pharmacy, visiting a coffee shop, getting a haircut, or visiting friends. The more activities you engage in and the greater their frequency, the greater the risk of being infected.

The calculations show that getting people back to work safely will be a challenge until a vaccine is developed. Until then, for the workplace to be safe, the chance that a person becomes infected in a single day needs to be extremely low, because each worker faces that risk every day. That means putting in place rigorous safety precautions plus frequent testing.

Keep this in mind before venturing out too soon *or* too often: COVID-19 risk not only depends on what you are doing but also how often you do it. Stay safe!