COVID-19 Classroom Calculator

Disclaimers: I am not an epidemiologist, and this math has NOT been double-checked by anyone. If you see an error (or there's an assumption you'd like to be able to edit that you can't currently) feel free to contact me via email: pmawhort (at) wellesley.edu.

What is the probability per class meeting that you will have a student who is actively transmitting COVID-19 in your classroom? This calculator attempts to answer that question by combining data you enter about the prevalence of COVID-19 in your school and your classroom size. Note that it does NOT attempt to calculate the risk of actually catching COVID-19: a site like microcovid calculator can help you estimate that, although it involves a lot more assumptions. In general, if everyone in a classroom is masked and vaccinated and if there's good ventilation, the chances of it spreading in the classroom even when someone infectious is present are not necessarily high.

Obviously faculty and staff are potential sources of infection as well as students, but accurate numbers for their COVID-19 rates are often less available. This calculator only takes students into account, although if you have faculty data you can simply increase the school population and students/class numbers to include them.

How many students are at your school (enter an integer)?
How many new student COVID-19 cases occur each week (enter a number)?
What percentage of students are vaccinated (enter a number between 0 and 100)?
How many times each week does each student take a test if they don't have symptoms? (enter a number; enter 0 if there's no asymptomatic testing)
For how many days do students quarantine after a positive test? (enter a number)
How many students are in your class? (enter a whole number; feel free to enter the total number of students in all your classes to compute the probability of an infectious student in any class, but only count each student once if some students are enrolled in multiple sections you teach)
How many times does your class meet in an entire semester?

Assumptions about disease transmission (click to expand)

You can change these from the defaults (based on this article) if you want to model different scenarios. Although infectiousness actually gradually decreases with time, to simplify things we are modelling it as a binary yes/no variable which completely cuts off after a certain amount of time. This is one way in which this calculator is definitely not accurate. Also note that different people have different levels of infectiousness, and for example, being vaccinated reduces infectiousness. We do not model that, since we're only trying to calculate the probability that an infectious individual is present, not exactly how infectious they are. How many days on average does a non-vaccinated person remain infections (enter a number)?
How many days on average does a vaccinated person remain infectious (enter a number)?
What percentage of unvaccinated cases are asymptomatic? (enter a number) (Sources include: example of a single study; a meta-analysis; discussion of many studies; we use 40 instead of 35 since the student demographic skews younger.)
What percentage of vaccinated cases are asymptomatic? (enter a number) (one source on asymptomatic cases in vaccinated individuals shows about the same as above, but another study shows odds ratio of ~2 (i.e., 2x more likely to be asymptomatic) for vaccinated individuals; as a perhaps optimistic estimate we just set this slightly higher than for unvaccinated cases.)
By what percentage does being vaccinated reduce the risk of infection? (enter a number between 0 and 100) (source for default value)

Based on the numbers you entered above, here's what we compute:
The average number of days of infectiousness per case for four conditions based on vaccinated/unvaccinated and symptomatic/asymptomatic. This takes into account vaccination status, testing, and isolation periods; the numbers are:
For vaccinated, symptomatic cases: ? days/case
For vaccinated, asymptomatic cases: ? days/case
For unvaccinated, symptomatic cases: ? days/case
For unvaccinated, asymptomatic cases: ? days/case

Based on that plus your estimate of the number of infected people per week, the number of infectious people on campus each day is: ? cases/day
The contributions from various groups were:
For vaccinated symptomatic cases: ? cases/day
For vaccinated asymptomatic cases: ? cases/day
For unvaccinated symptomatic cases: ? cases/day
For unvaccinated asymptomatic cases: ? cases/day

Now that we have an expected people-infectious-per-day number, we compute the probability for a single class meeting that an infectious person is present:
First we compute the probability that any single individual student is infectious, and get: ?%
Using that number, we compute the probability that at least one person in your class is infectious (given the class size you entered above) which is: ?%
And if we extend that calculation to the whole semester, given the number of class meetings you entered above, we get the probability that at some point during the semester, there will be an infectious student in your classroom: ?%

Critically, because of asymptomatic cases, especially if your isolation period is decent, unless your asymptomatic testing is frequent, the likelihood is high that most of the infectious people in your classroom will have no way of knowing they are sick! The students are absolutely blameless in this model, because asymptomatic infections are by definition undetectable without regular asymptomatic testing.