Post #1117: William and Mary, another good day, the math of herd immunity.

Today’s test results were 1-for-1772.  Three days of census testing are highlighted in yellow below.  In short, they’ve tested three-quarters of campus enrollment and found one COVID-19 case.

Again, obviously good news.

This is a follow-up to my last post, and in this I try to explain why you might not want to, or be able to, relax the William and Mary COVID-19 hygiene rules just yet.  Despite this good news. Continue reading Post #1117: William and Mary, another good day, the math of herd immunity.

Post #1115: William and Mary, zero cases in a further 1599 tests? Sure looks like herd immunity.

Edit:  Oh, no.  My wife tells me this is prompting calls to ease up on the COVID-19 hygiene at William and Mary.    I know it’s tough to grasp, but that arithmetic of epidemics says that would be unwise. 

It’s too late this evening, but I’ll write up the math on that one tomorrow.  Until the virus is no longer in circulation anywhere, the way you keep it from entering and spreading in the W&M student body is via the combination of vaccination and COVID-19 hygiene.  I realize that “herd immunity” is rarely discussed this way, but it’s the combination of those two effects that reduces the transmission rate enough to get you over the herd immunity threshold. 

You risk firing this right back up again if you drop the COVID-19 hygiene portion of this system, given the incidence of new cases in the community.

Original post follows:

Yesterday W&M reported zero new cases in 1488 tests.  Today they reported zero new cases in a further 1599 tests.

Like so:

It’s extremely unlikely that we would observe this, if the recent rate of new infections was continuing.  That’s what yesterday’s math showed. Continue reading Post #1115: William and Mary, zero cases in a further 1599 tests? Sure looks like herd immunity.

Post #1113: William and Mary, zero cases in 1400+ tests. Herd immunity?

William and Mary has started another round of “census” testing, administering COVID-19 tests to all students on the campus.  Yesterday, an email from the W&M administration said that test results should start appearing on the W&M COVID-19 dashboard.  And they have.

Yesterday, W&M reported test results for 1448 students.  They found no (zero) positives.  Zero new COVID-19 cases, out of 1448 tested. Continue reading Post #1113: William and Mary, zero cases in 1400+ tests. Herd immunity?

Post #1110: William and Mary, no COVID-19 uptick following spring break days

William and Mary had a COVID-19 outbreak following St. Patrick’s day.  There was some concern that we might see another such outbreak following two back-to-back spring break days last week (April 6th and 7th).  In my last post (Post #1099), I said I’d check in again to see whether there was an uptick following spring break.  Continue reading Post #1110: William and Mary, no COVID-19 uptick following spring break days

Post #1098: William and Mary update to 4/5/2021

William and Mary added another 200 tests and ten new positives to their COVID-19 dashboard count on Monday.

I’m not quite sure what to make of that, but I’m going to take a guess.  While it superficially looks like bad news, I’m guessing that it really isn’t.  I’m guessing that this most recent Monday figure should best be compared to last Monday.

What’s the reasoning behind that?  In a nutshell, I’d bet that Monday has three days’ worth of bad news rolled into it.  Continue reading Post #1098: William and Mary update to 4/5/2021

Post #1084: William and Mary brief COVID-19 update

I’ve added another day’s worth of testing information to my prior table.

The surprise here is that they added fewer than 200 new test results yesterday.  They still don’t have tests back from what appears to be about one-sixth of the students.

It’s not clear to me what that means.

On the one hand, they might just be waiting for the lab performing the tests to return results.

On the other hand, maybe a lot of students aren’t cooperating with the testing.  I looked on the William and Mary website and all I could find is the phrase “testing is required”.  I can’t see anything about (e.g.) penalties for non-compliance.

On yet a third hand, maybe the total count of students ever tested (on the W&M COVID-19 dashboard) is significantly larger than the count of persons required to be tested.  That seems unlikely, as W&M appears to make few exceptions to its testing requirement.   The make “limited exceptions for students enrolled in certain graduate programs“.  But there’s no public information on the number of such students exempt from the testing requirement.  They also exempt persons who have tested positive, for 90 days following a positive tess, due to the likelihood of a false positive test during that period.

So it’s not crystal clear, but it certainly looks like test results are still pending for more than 1000 students.

Post #1078: W&M St. Patrick’s Day outbreak, updated


William and Mary updated their COVID-19 dashboard at close-of-business yesterday (Friday, 3/26/2021).  They normally don’t update it over the weekend, so that should be the last count of COVID-19 cases we’ll have until Monday evening.

Yesterday’s update was in line with expectations.  Each new batch of tests results is showing that more-or-less a steady 1.4% of students test positive for COVID-19.  Assuming that holds, by the time all the test results are back, they’ll have had just under 250 known on-campus positives this semester.  Unless the lab they are using closes for the weekend, that’s about how things should stand on Monday. Continue reading Post #1078: W&M St. Patrick’s Day outbreak, updated

Post #1075: William and Mary COVID-19 trends, not looking so good (St. Patrick’s Day outbreak).

This is the second edit of my original post.  The original post said, more or less, hey, there was an unusual jump in COVID-19 cases at William and Mary.  Why was that?  The first edit said, never mind, the W&M administration explained that cases rose as a result of testing everyone on campus.  And this edit explains that not only did cases jump, they are going to continue to jump over the next few days.

Why?  Looks like the same problem that has hit so many college campuses: Rapid spread of COVID-19 due to off-campus parties.  In this case, St. Patrick’s Day parties.

You have to give W&M credit.  Reading between the lines, they spotted this outbreak as students became symptomatic following St. Patrick’s Day.  And they’re now staging the full fire drill, starting with testing every student on campus, followed by quarantine and contact tracing.  This is just about as good as it gets, in terms of pandemic response.

Edit 2:  That said, as of COB 3/25/2021, the count of cases on the William and Mary COVID-19 dashboard stands at 197 cases total, with 57 active cases. 

And that won’t be the end of it.  Meaning, don’t panic (yet) as the numbers continue to climb over the next couple of days.

The email that was circulated by the W&M administration (see below) states that all students are being tested.  From that, it’s easy enough to calculate where this is heading.

So far, they’ve gotten back about half the tests (just over 3000).  They’ve added 43 cases, based on those first 3000 tests.  The natural assumption is that they’re going to find just about that many again when the rest of the tests come back.

You can reasonably expect another 40-ish cases to show up  on that dashboard over the next few days as the rest of test results coming back.  By the time all the tests come back, the total should be up to 250, possibly with around 100 active cases.

And then, even though they are testing all students, there will still be some infectious students circulating in the student body.  The reason for this is that COVID-19 PCR testing has a fairly high false negative rate.  (See Post #859, or the graph just below).  So, even after this round of testing, there will be a non-negligible number of undiscovered infectious individuals on campus.  If I had to guess, if they find 100, using PCR testing, they likely missed at least 25, for an overall false-negative rate of 20% (25/125).

So in addition to the lump of cases that’s showing up right now (and for the next few days), there should be a fairly long “tail” of new cases, from this outbreak, that will trickle out slowly, from the cases that PCR testing inevitably will miss.

To give this a name, let me dub it the “St. Patrick’s Day outbreak”.  The email from W&M implicates off-campus St. Patrick’s Day parties, and subsequent socializing, for this uptick in cases.  The timing seems about right for that, given that there’s a median five days between infection and onset of symptoms, for symptomatic cases.

William and Mary has now experienced the same problem as so many other colleges:  Rapid spread of COVID-19 via off-campus parties.  They had some of that at the start of the Fall semester.  I think this is the first time this has happened mid-semester.

Addendum:  COVID-19 PCR test false negative rate.  A false negative occurs when a person has a disease, but the test does not detect it.  Here’s the graph showing the false-negative rate of COVID-19 PCR (DNA) testing, by days following infection.  This exact rate shown depends on the population used to create this graph, but the general gist of it is the same for any population.  For the first couple of days after infection, you won’t test positive for COVID-19, even though you have it.  By the time you’re four or five days into your infection, the odds of a positive tests are better, but still not 100%.  And then, as you proceed further past the date of infection, the odds of false negative begin rising again.

Source: “Variation in False-Negative Rate of Reverse Transcriptase Polymerase Chain Reaction–Based SARS-CoV-2 Tests by Time Since Exposure:, Kucirka, Lauren M, Lauer, Stephen A, Laeyendecker, Oliver, Boon, Denali, Lessler, Justin doi: 10.7326/M20-1495 Annals of Internal Medicine, May 13 2020,

Edit 1:  Ignore the rest of this post.  The College of William and Mary sent out an explanation by email this afternoon.  The uptick is plausibly attributable to re-testing everyone on the campus.  Here’s an excerpt from the email:

Dear W&M Community,

William & Mary is undergoing a round of census COVID-19 testing of all students living on campus and in the vicinity. With roughly a third of results received, the university has seen a significant uptick in positives within the student population. We continue to update the COVID-19 dashboard to reflect current results every weekday. We anticipate this number to grow as additional results are returned, which is why we are contacting you today.

That’s the first such email I’ve received, I think, but the body of the email suggests that they’ve been sending these out all along.

Original post follows:

I’ve been tracking the COVID-19 case count at the College of William and Mary, comparing the actual case count (blue bars above) to an “expected” case count, based on the COVID new case rate observed for Virginia residents age 20-29.

A week ago, actual cases were about 15% below the expected level.  But as you can see above, there was a spate of new cases at William and Mary in the past week or so.  As a result, the actual case count (blue bars) is now back up to the “expected” level.

That’s not good.  And that comes as something of a surprise.

Plausibly, this might just be some one-off event, such as an un-publicized outbreak on some sports team.   But I’m not seeing any news reporting on this, nor did I find any explanation on the William and Mary website.   In terms of public information, I’m not finding anything to explain it.. Continue reading Post #1075: William and Mary COVID-19 trends, not looking so good (St. Patrick’s Day outbreak).