What is the actual infection rate at universities?

Here’s a question: what fraction of students at MIT have COVID-19 right now?

Since MIT tests students twice a week, this question should be pretty easy to answer. But it’s not.

That’s because MIT, along with other universities in the area, doesn’t report their infection rate. What they report is the positive test rate.

The Positive Rate is computed as

At first glance, this might sound like the fraction of the population that has the virus, but it’s not. That’s because, once you test positive, you don’t get any additional tests for 14 days (the length of a quarantine). That means that, in the time that a normal person would have gotten tested four times, an infected person only gets tested once. The true percent of the MIT population with coronavirus is probably more like

In my view, that’s pretty bad. Roughly speaking, this suggests that every two weeks, each student has a chance of getting the virus. If a student lives at MIT for a year, their chance of avoiding the virus extrapolates to

So, by the end of the year, we may be looking at roughly 20% of MIT’s population having had the virus.

Of course, my extrapolation could be way off. But that’s the problem: MIT should be providing data that makes it easy to perform this sort of extrapolation, and they’re not.

Other schools are doing the same thing. Here’s Northeastern University’s infographic.

In my opinion, this graphic crosses the line to intellectually dishonest. The sea of blue is intended to comfort the reader without providing any useful information.

This is incredibly harmful. I’ve heard first hand from students who are convinced that the virus risk is low enough that they should just continue business as usual. Graphics like the one above inappropriately perpetuate that belief. In a crisis where bad math can literally kill, universities should do better.