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Modeling personal risk of contracting COVID19 while attending university classes

Using a new model of exposure risk to estimate the chances of contracting COVID19 if attending in-person classes this fall

Paying attention to ventilation in classrooms

One factor in particular that has been concerning me is the rate at which potentially contaminated air in enclosed spaces is replaced with clean air, and how this in turn impacts potential risk. As a result, I’ve been pleased to see a growing body of preliminary research looking at just this — including a recent pre-print on medRxiv from Dr.Shelly Miller at the University of Colorado, Boulder, and her colleagues, on COVID19 transmission associated with the Skagit Valley Chorale superspreading event.

Modeling in-class COVID infection rates

The model is based on the spread of fine airborne microdroplets (aerosols) containing COVID19 in enclosed spaces, and the accumulation and inhalation of these over time. It assumes that these aerosols are so fine that they rapidly mix and spread through the whole volume of a room (which is reasonable), and so the physical distance between people in the room becomes less important than how rapidly the contaminated air is replaced by clean air.

Modeling of Personal Risk of Becoming Infected

Fortunately, the model allows a crude estimate of personal risk of developing COVID19 if one of your class mates is a spreader, with the addition of a few lines of calculations.

Preparing the Model

Dr. Jimenez’s model allows users to alter a number of key parameters including:

  • Number of instructors and students;
  • Class duration;
  • Air exchange rate (or clean air supply rate per person); and
  • Mask efficiency.
  • The individual risk of becoming infected if the course instructor or another student are infectious.


Risk versus room occupancy

First off, I ran the model to explore personal COVID19 infection risk in a large auditorium (900 square foot) and a small classroom (250 square foot), each with a range of students physically present in the class (figures 1 and 2 below).

Figure 1. Personal risk estimates for a 900 square foot class room as a function of occupancy.
Figure 2 Personal risk estimates for a 250 square foot class room as a function of occupancy.

Masks versus no-masks

I included risk estimates with and without masks here, as I’m pretty sure that, despite current requirements on most campuses, students and instructors are going to discover very rapidly that teaching large groups (especially where there is a lot of discussion) for 2–3 hours where everyone is masked, is going to be extremely challenging. And the more challenging it gets, the more temptation there’ll be to remove the masks.

Increasing room size while keeping occupancy fixed

I next ran the simulation for a fixed number of students (15) taking classes in rooms of varying sizes, to explore how room size affects risk. In all cases I stuck to the ventilation rate of 5.7 air exchanges per hour (remembering that this assumes clean air coming into the room).

Figure 3 Personal risk estimates while varying room size for a fixed number of occupants

Varying Ventilation Rates

An alternative to increasing room size or reducing occupancy, is changing the air exchange rate. This will not always be possible, or even advisable as rooms and HVAC systems are designed and set to specific standards. But just to see the potential impact, figures 4 and 5 show the potential impact of changing the ventilation rate in a large auditorium and a small room.

Figure 4. Estimating personal risk in a 900 square foot classroom for a range of air exchange rates.
Figure 5. Estimating personal risk in a 250 square foot classroom for a range of air exchange rates.

Expanding Risk Reduction Scenarios

Beyond the scenarios above, the model is also useful for exploring other risk reduction scenarios. For instance, what if classes were split so that 50% of students attended in person and 50% attended online, or in-person classes were halved in length with additional instruction occurring online and/or asynchronously, or in-person classes were only held every other week.

Figure 6. Estimating personal risk in a 900 square foot classroom for four different scenarios.

Variable community infection rates

Finally, I wanted to get back to the somewhat arbitrary use of 0.3% as the estimated percentage of students and instructors who unwittingly come to class while infectious.

Figure 7. Personal risk estimates as a function of the percentage of students attending class who are infectious

Proceed With Caution

Of course, this assessment should be taken with a large pinch of skepticism. As researchers and risk managers get a better handle on the necessary parameters, estimates of risk may go up as well as down. Yet it does indicate that the risks of infection through in-person classes is not insignificant, and care is going to need to be taken as students come back to university. It also suggests that innovative approaches are still needed to reduce exposure through the creative use of distance learning, and that simply assuming that wearing masks and keeping distant from others in class will do the trick.

Update on calculations (July 3, 2020)

As was noted in the comments on the original post, the expression for estimating semester-wide risk used above is not correct, but is rather a somewhat naive simplification that falls apart when in-class risks are high, and the number of classes taken is high.



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Andrew Maynard

Scientist, author, & Professor of Advanced Technology Transitions at Arizona State University