Post #1242: COVID-19 at William and Mary, some clarifications.

Posted on September 10, 2021

In my last post on this topic, I had a hard time making sense of the numbers regarding COVID-19 cases at William and Mary.  Now I know more, and I’m passing that along.

All Virginia colleges are having some problems with COVID-19 this semester.  But  William and Mary appeared to have a worse-than-average problem, relative to the size of the  on-campus population.  They seemed to have more cases than you would expect for the Virginia college-age population as a whole, and more than appeared in the handful of universities I used as a comparison group.

Skip the next section if you just want to get to the numbers.  But in fact, the graphic above tells the story.  That’s why W&M is counting so many positive cases, relative to the number of persons they have tested.

Background:  Deja vu all over again.

To be clear, William and Mary has emphasized that (as of three days ago) “all of those cases are experiencing no or mild symptoms.”  W&M’s contact tracing indicates that “All cases … spread through unmasked social interactions – often off-campus.”  I take the last part of that to be a euphemism for parties.  And that ” … there is no indication of spread in a classroom.”  (Source:  William and Mary messages to students.)

By my recollection, this is virtually identical to the situation last semester.  Parties were the problem.  (In particular, St. Patrick’s Day parties).  Classrooms were a non-issue.  And, unstated but probable, there is some amount of secondary spread by unmasked close contacts.  We know that COVID-19 spreads to a modest degree within households with an infected person (so-called “secondary attack”), I am guessing that some modest portion of the spread is within dorm rooms and suites.  I have seen nothing that directly verifies that.  But, presumably, that’s where most of your unmasked on-campus social interaction takes place.

As near as I can tell, this is the typical pattern for most U.S. colleges and universities.  So there’s nothing new here, either compared to W&M’s recent past or to the cross-section of U.S. colleges.

Really, the only changes from last year are that almost everybody is vaccinated to some degree, and the Delta variant is significantly more infectious (transmissible) than the Alpha variant which became prevalent prior to last semester’s St. Patrick’s Day outbreak.

Near as I can tell, those two factors — vaccination versus greater infectiousness — roughly cancel out, in terms of impact on spread of disease.  Vaccines reduce it, the greater infectiousness of the Delta variant increases it, and just by chance, they have roughly equal effects at the vaccination rates seen in the general population.

Given that, and given the high incidence of COVID-19 in the community generally, it’s not surprising to see some spread of COVID-19 on the W&M campus.  It’s not even really a surprise to see an outbreak, that is, multiple related cases occurring at the same time.

For what it’s worth, based on the calculations I’ve presented in this blog from time to time, the high vaccination rate on the W&M campus, combined with masking in social situations, should have prevented this outbreak.  Even with the higher infectiousness of the Delta variant.  Even with the lower efficacy of vaccines against the Delta variant.  So, to me, at the end of the day, it’s the “unmasked” part of the “unmasked social interactions” that’s the root cause.  The 93% vaccination rate plus rigorous COVID-19 hygiene should have made the campus immune to outbreaks.  But without the additional exposure reduction from masks, the 93% vaccination rate alone is right on the edge of being adequate to suppress a Delta variant outbreak.   You can see the rough calculation in Post #1160.

This is why you no longer hear anybody talking about “herd immunity”  any more.  Practically speaking, it’s impossible to achieve herd immunity (in the sense of “we can all go back to normal now and quit using masks”) in the general population with the Delta variant, given the efficacy of current vaccines.  You’d have to vaccinate people at gunpoint to achieve the >91% vaccination rate required.  At best, we can hope to use vaccines to reduce the size, extent, morbidity, and mortality associated with outbreaks.  But we aren’t going to be able to vaccinate enough of the general population to prevent outbreaks, absent some permanent and enforced mask mandate on top of the vaccination.

As was true last year, W&M administration has tightened up the rules in an attempt to stop this latest outbreak.  Indoor dining has been suspended.  Mask mandates have been expanded to include outdoor situations where you can’t maintain social distance.  If I had to guess, I interpret that last one as an attempt to avoid large unmasked crowds at (e.g.) sporting events.  Nothing could possibly look worse on the news than a big outbreak in the student population superimposed on a stadium full of unmasked cheering students.

My only point is that, in terms of COVID-19 levels on campus, the main difference between this year and last year is that there’s so much COVID-19 currently circulating in the general population.  We’re starting off from a much higher base rate of infections that was the case last semester.  The red circles show school opening last year versus this year.

Otherwise, near as I can tell, Delta variant versus vaccination rate is more-or-less a case of offsetting effects.  Unmasked parties are the problem.  Classrooms aren’t.  Deja vu all over again.

Explaining the numbers.

William and Mary is counting all positive cases regardless of the source of information that a person is COVID-19 positive.   The count of COVID-19 positives includes individuals identified by William and Mary testing, and individuals identified by any other testing, including all individuals who self-identify as COVID-19 positive.

The count of tests, however, is just the count of tests administered by William and Mary.  It doesn’t even include the count of persons identified as positives via other testing or self-identification. 

The short answer is that you can’t calculate anything like a test positivity rate from those numbers.  The numerator effectively includes everyone.  The denominator includes that small subset of students tested for having close contacts with a known COVID-19 case.  To take it to the level of absurdity, there’s nothing that prevents the count of positives from exceeding the number of persons tested.

Further, it’s hard to be sure that I can legitimately compare the W&M number to other colleges and universities.  I’d have to find out the details of what they are reporting.   If a college is doing “screening”-type testing, and only reporting positives found by that, it’s not clear the results of that would be comparable to the results from William and Mary’s current approach.

The current W&M approach — count all positives from any source, only test individuals with known exposure — should yield a per-capita rate of infections that’s modestly higher than that found in the community.  All other things equal.  In effect, this is testing-for-cause, plus attempts at contact tracing for 100% of known cases.  What we have in the community is testing for cause, plus contact tracing for maybe 50% of known cases (see Post #1197).  If the underlying rates of infection are identical, we’d expect a modestly higher rate of new cases to be discovered in the W&M population.

That said, newly discovered infections continue apace.  I interpret the table below as showing that they’re still identifying cases from the initial outbreak.  I specifically don’t interpret these three days’ of data as showing that the outbreak is getting worse.

In any case, here’s the last three days of data from the William and Mary COVID-19 dashboard.  The rate of new case discovery per 100,000 population is very high, compared to what’s going on in the community.  I think that’s expected at the positive tests come in from the start of an outbreak.  It’s not good, but we’ll need to give it a few days to see whether or not this will slow down to a more normal level.

For what it’s worth, we can the current rate of daily new cases to last semester’s St. Patrick’s Day outbreak.  The chart below is my from my final look at that outbreak.


As you can see, the increase in positive cases that William and Mary is seeing currently (call it 23 per day, for the past two days) is about what they saw during the heart of last spring’s St. Patrick’s Day outbreak (circled above).

The upshot is that the current outbreak is as bad as, but no worse than, last semester’s St. Patrick’s Day outbreak.  Deja vu all over again.