Post #1000: The simple arithmetic of the U.K. coronavirus variant

Posted on February 8, 2021

Today’s numbers.  Looks pretty good.

But not good enough.  They aren’t good enough, as they currently exist, to prevent a fourth wave of COVID, from the U.K. variant.

But don’t freak out just yet.  FWIW, my calculation is that if we merely stay the course — keep vaccinating at the current rate, maintain existing COVID hygiene — the inevitable spread of the U.K. variant will merely cause a slowdown in our recovery, and need not cause a fourth U.S. COVID wave.

Details follow.

We’re now winding down the third wave of COVID.  It’s not crystal clear why.  I argued back on 12/28/2020 that some combination of herd immunity and the natural seasonality of coronavirus shifted the odds in favor of decline.  We were due to hit a peak.  The peak of the U.S. coronavirus third wave occurred on 1/8/2021, and we have seen steady, nation-wide declines in new cases since.

It’s not crystal clear exactly what factors are causing the current decline.  It’s not (yet) behaving as it should if herd immunity were the dominant factor.  In prior posts, I argued (with numbers!) that herd immunity (from infections) plus herd immunity (from vaccinations) ought to result in a rapidly-accelerating end of the third wave. 

But so far, eh, maybe the rate of decline sped up a bit, starting 2/1/2021.   There could be a lot of reasons for the lack of a clear acceleration, starting with “I might be wrong”.  But possible reasons also include the six-week lag between first vaccine shot and full immunity.  And until those vaccinated individuals get out there and circulate in the general population, they won’t play a significant role in stopping the overall growth in new COVID cases.  (Which is why you needed to have invited Grandma to your Superbowl party, per the just-prior post).

Numerically, right now (as of 2/7/2021), the effective (observed) viral replication factor is about 0.85.  That’s my estimate, based on data starting 2/1/2021.  Under the assumption that each generation new infections takes an average of about 4.5 days, and we’re seeing a decline of 23% per week starting 2/1/2021, then “R” is (0.77 ^ (4.5/7) = ) 0.85.  (Where “^” is “raised to the power of”).  In other words, a 15% reduction in new cases every 4.5 days (R-effective) is the same as a 23% reduction in new cases every 7 days.

The bad news is, that’s nowhere near good enough to contain the U.K. variant of the coronavirus.  Which, per news reports, is doing what it was expected to do, and taking over the U.S., same as it did Great Britain.  For the simple reason that it’s more infectious, easier to spread.

It’s often stated that it “out-competes” other strains, but I think that’s a misnomer.  It simply spreads faster than other strains, and so becomes an increasing share of the new case total.  You really ought to think of it as if there were now two completely separate pandemics going on.  One with the strain that has been prevalent all along, and now a new pandemic, with a new virus that is easier to spread.  As the old pandemic with the old virus is winding down, this new pandemic is just getting started.

So let me now just present some arithmetic.  Let me get the facts straight about a snapshot of the current situation.  And then talk about how long we have before the U.K. strain takes over, and what might change to improve the situation in the meantime.

The research.

The most current research is here.  And as is so often the case, you need to read it detail (download the .pdf from that web page) to get the relevant details.  But if you prefer the popular press writeups, here’s Slate, here’s the Washington Post.

I’m not going to worry about the fine points but I am going to worry a lot about the dates.  U.S. reported cases underwent a sea-change circa 1/8/2021, and anything measured before then need to be adjusted accordingly.

Their detailed data analysis starts on 12/15/2020.  They last day of actual data observations is 1/30/2021.  (The last two weeks involves an extrapolation,  but I think that’s harmless.  The key point is that they did, in fact, measure the key marker for the new variant through 1/30/2021.)

Then:  “the proportion of B.1.1.7 cases reached 3.6% in the U.S. by the last week of January, 2021″

Second, they project (using what looks to be a fit to a standard logistic curve) that this new variant will account for half of new U.S. cases as of March 21, 2021.  That’s based on:

  • Logistic growth rate of 7.1%/day.
  • Increased transmissivity of 35% – 46% higher than existing strains.
  • Doubling time of 9.8 days.

I started to see if I could square that with the numbers I’ve been calculating for the existing strain, but I’m completely unsure of the arithmetic here.  I am nevertheless going to take a shot at it, using the transmissivity figure.

Right now, I estimate the effective “R” (transmissivity) of the current strain at around 0.85, as noted above.  If that increases by 40%, that would yield 1.19, or a weekly growth rate of 1.31 or 31 percent.

But in fact, by March 21, the U.K. strain will only account for half of cases.  Cutting the estimated transmissivity increase in half yields weekly growth of just 1.03 or 3 percent.  Just starting to climb.

The upshot is that, if we don’t see a faster rate of decline in new cases soon, we can expect the 4th wave of COVID to begin around the second week of March That’s the point at which new cases will stop declining, and start rising.  Where the composite “R” value, for the mix of cases projected for that time, will be just about 1.0.  One new infection for every existing active infection.

The second thing to asks is, how much of a decline in new cases would we need to see, with the existing strain, to know that the current combination of seasonality, herd immunity, and COVID hygiene would be enough to contain the new U.K. strain?

The quick answer is that new cases need to fall more-than-twice as fast, as they are falling now, in order to nullify the increased transmissivity of the new strain.  Right now, R = 0.85.  But you need R = 0.70 if you want that projected 40% increase to lead to no growth.  (That is, 1.40 x 0.70 =~ 1.0).

The practical upshot of that is that, with the currently prevalent strain, we need to see new cases falling roughly 45 percent per week, to say that we’re in good shape to withstanding the U.K. variant without a fourth wave.

(That’s calculated as 0.70^(7/4.5), to get the weekly growth rate for new cases from the needed transmissivity factor R.)

That’s the figure we’d need with the current strain.  That target rate increases as the new strain takes over, and it should be close enough linear that it hardly matters.  Right now, the U.K. strain is rare enough that it doesn’t matter empirically.  As we move into March, that changes, and we can tolerate rates above -45% per week and still say that we’ve got things under control with respect to the U.K. strain.

Factors in our favor:  Herd Immunity and Seasonality

The upshot of all the above is that things look pretty good right now, but they aren’t good enough.  They aren’t good enough to keep the pandemic in check as the U.K. variant takes over.  So either we get better at interrupting infections now, or we suffer the consequences later.

One thing in our factor is the growing level of herd immunity.  By mid-March, if current trends more-or-less continue as they are now, I would project as below.  This assumes a continued 1.5M vaccinations a day, and a continued 23%/week decline in new COVID cases.

That would help materially to reduce new case counts.  Note that most of the growth in new immunity at this point is via vaccinations.

(And as I have noted earlier, it would also help materially if the CDC would not insist on vaccinating individuals who have already recovered from COVID. Or, if they’d at least ship more vaccine to states with the highest proportion of population with no immunity.  But, no to both.  Each state gets the same number of doses per capita, and each person gets two shots whether they’ve already had COVID or not.  Right now, when the vaccinated portion of the population is small, this doesn’t much matter.  But as you can see from the “unduplicated” line on the second table above, if CDC would not “duplicate” the immunity by vaccinating individuals who have already had COVID, we would end up with 64% immune, not 56% immune, which would be a nice cushion.  I should also note that I am not the only person to have figured this out and advocate for reduced vaccination of persons who have recovered from infection last.)

I’ve already done the math to allow me to calculate the impact that would likely have, a couple of ways.

Using the algebra in Post #984 (“Now look what happens when …), with the increase in the immunized population and no changes in COVID hygiene, I project an R-value of 0.67.  Using the algebra of Post #991, I get a projected R of 0.69.

That should, by itself, be enough to keep the U.K. variant in check.  It takes a while for full immunity to develop.  But, on the other hand, the U.K. variant will only account for half of new cases at that time.

Upshot:  My back-of-the-envelope says that if we keep vaccinating individuals at the current rate, and don’t slack off on COVID hygiene, we will beat the U.K. variant via herd immunity alone.

The other thing to keep in mind is the inherent seasonality of coronavirus.  Or, putting that another way, the anticipated decline in the transmissivity of all coronavirus strains as we move from winter to spring.

As a whole, incidence of all types of human coronaviruses peaks in February in the Northern Hemisphere (see this recent meta-analysis, or this one, regarding seasonality).  And judging from the graph below,  which show proportion of respiratory illness attributable to all coronaviruses, worldwide, it’s reasonable to expect significant declines in transmissivity purely as a result of seasonality.

Source: Global Seasonality of Human Coronaviruses: A Systematic Review Sangshin Park,Yeonjin Lee,Ian C Michelow,Young June Choe Open Forum Infectious Diseases, Volume 7, Issue 11, November 2020, ofaa443, Published: 18 October 2020

So, the odds are that we’ll get a material boost from the natural seasonality of coronaviruses.  On top of the buildup of herd immunity, now largely occurring via vaccination.


The bottom line on questions like this is that you have to form your own judgment.  The news media are only interested in fear-based journalism.  The CDC literally has  duty to lie to you if that will benefit the public health.  (And, separately, a bureaucratic imperative to tell you only things that will encourage you to get vaccinated.)

So I took my best shot at it.  Yes, the U.K. variant appears to spread much more easily than the existing prevalent U.S. strains.  Yes, under current conditions, that means we’d have a fourth wave of COVID.

But no, I don’t think we’re going to have that fourth wave.

As long as we can keep our act together for another couple of months.  Admittedly, this is more than many Republican state governments can manage.  But I think those of us with sensible state governments can probably maintain the status quo for that long.

And as long as vaccinations continue apace.  Even based on the most pessimistic surveys regarding intent-to-vaccinate, we will not have come close to exhausting the U.S. adult population that intends to get the COVID vaccine by mid-March.

It would not hurt if everybody upgraded their masks in the meantime.  As many European countries are trying to do. I need to do another catch-up on N95s available via Amazon, because it looks like some more cracks have developed in the embargo on retail sales of N95s.

But we have one great advantage in the U.S.  We so thoroughly messed up our initial response to COVID that we now have a very large pool of people presumed immune via having already been infected.  And now we get to benefit from that.

The CDC keeps repeating the party line, which is that we need 70% vaccinated to end the pandemic.   I keep pointing out why that’s simply wrong, as a matter of basic epidemiology.  We need the combined effect of herd immunity from all sources, plus COVID hygiene, to generate an effect equivalent to 70% vaccinated.

If the CDC really were correct, we’d be up a creek regarding the U.K. variant.  If they were right, a big fourth wave is already baked in.  And so, I can now say, not only are they wrong, but thank goodness they’re wrong.