Post #1051: U.K. COVID-19 variant versus the U.S. COVID-19 vaccination rate.

Posted on March 11, 2021

Data sourced from the Helix® COVID-19 Surveillance Dashboard. Accessed at on 3/11/2021.

If you care about the details, read the caveats on the Helix COVID-19 dashboard.  This is from a sample of convenience, it’s not guaranteed to be representative of all cases (not even with in a state, let alone within the U.S. as a whole).  But I think it’s the best data available for estimating the U.S. incidence of the presumably more-infectious U.K. COVID-19 strain B.1.1.7.  And, whatever the bias in the estimate at any point in time, this should still provide a consistent estimate of the trend over time.  As of 3/8/2021 sample collection date, table “Daily Percent SGTF of Positive Samples”

U.K. COVID-19 variant as percent of new cases:

  • U.S., 32%
  • Florida, 52%

(I use the most recent one-day reading here because the five-day moving average is biased downwards due to the high rate of growth of these numbers.)

This is more-or-less as expected.  As explained in earlier posts, my “simple model” for the growth of the U.K. variant runs a bit too fast.  I would have expected something just over 34% for the U.S. by now.  Still, we’re in the same ballpark.  This simple model remains an adequate tool for thinking about the spread of the U.K. variant in the U.S.  And the U.K. variant is spreading at more-or-less the expected rate.

If it’s a horse race, why are our horses still winning?

New case counts are now 78% below the peak.  New cases are falling in all regions.  Each day, the majority of states sees a reduction in new cases from the prior day.

Source:  Calculated from NY Times Github COVID-19 data repository, data reported through 3-10-2021.

If the U.K. variant is (say) 40% more infectious than the older COVID-19 variants it displaces, why aren’t new case counts rising?  In particular, why isn’t there any obvious change in trend in Florida?  But we can ask the same question of New York (with its own home-grown more-infectious variant), and California (ditto).

Here are Florida, NY, and California, graphed on log scales.

Possible explanations include at least the following.

  1.  It’s too soon to tell
  2. Vaccinations
  3. Seasonality (aka, stuff happens).
  4. It isn’t really that much more infectious

I think I can now start to dismiss option 1, too soon to tell.  That’s why I’ve been tracking this, and why I fixate on Florida.  If Florida really has reached the point where the U.K. variant accounts for 50% of new cases, all other things equal, the line graphed above (brown) ought to start bending up.  Maybe it is, maybe it isn’t.

I think option 3, seasonality is running the show, both here and abroad, but that still doesn’t explain why there’s no systematic differential across the states.  If you just google up the COVID-19 rates for the U.K. and Canada, you will see that the timing of the infection points for their curves, of late, is more-or-less an exact match for the U.S. curve.  While we’re still at the mercy of whatever coronavirus season wants to do, that doesn’t explain why Florida continues to behave just like the rest of the U.S.

I’m just going to dismiss 4, it’s not that infectious, out-of-hand.  I have no basis from which to second-guess experts in both the U.K. and the U.S.  Plus, to be honest, just from a common-sense perspective, it’s hard to grasp how it could be taking over if it weren’t more infectious.

Option 2, vaccinations, is plausible, but just doesn’t seem to be of a large enough magnitude.  But then again, maybe that’s just sloppy thinking. 

The sloppy thinking in this case is that the U.K. variant is supposed to be 40% more infectious, but we’ve only vaccinated 19% of the population, of which just 10% are fully vaccinated.  (And most of those are elderly who largely would not have been disease carriers under current circumstances anyway.  Right now more than 60% of the U.S. 65+ population has had at least one vaccine injection).  And so, crudely put, 40% wins, right?

Not so fast.  While there are a lot of un-quantifiable factors involved, the math in this case gets highly “leveraged” as the population approaches herd immunity.  If you start off somewhere near a steady state, adding just a few more immune people to the mix can make a fairly big difference.

That’s the point of the math in Post #984.  Immunization on top of a pandemic that’s in a steady state ought to result in bringing the pandemic to a rapid end.  Let me now update that.

Back in late January, as new case counts were falling sharply, I estimated the R (effective replication) value at the time this way, in Post #984.

  • 3.33 * (1 – (.41 + .54 – .41*.54)) =~ 0.90


  • 3.33 = R-nought, the original (zero-precautions) viral replication factor.
  • .41 = 41% of the population immune via infection (or vaccination).
  • .54 = net effect of existing COVID hygiene (masking/distancing/etc.)
  • 0.90 = R effective, the actual observed viral replication rate.

Those values were “fitted to the data” as of that date, meaning, I did a plausible calculation and managed to match the (then-) observed rate of decline.

Just take that old calculation at face value for now, and ask a simple question:  If I were to update that — for the spread of a more infectious COVID-19 variant, and for an increase in the fraction of the population immune — how would that effective R number change?  The real question being, is it even remotely plausible that vaccination is offsetting the effects of the (presumably) more infectious U.K. COVID-19 variant?

And the answer is yes, it’s plausible.  If we change the R-nought value to account for half the population having the more-infectious U.K. variant, but increase the fraction immune to 51%, we get roughly the same effective R-value.  Like so:

Obviously, there’s a lot of potential for slack here.  We ought to discount the vaccinated population owing to the concentration of vaccination among non-carriers of the disease (Post #1035).  We probably need to start dropping the COVID-19 hygiene factor owing to all the states that are dropping restrictions.  And, likely, the U.K. variant might or might not be 40% more contagious, as modeled.

Nor do I think this explains patterns of growth either across the states, or internationally.  (E.g., Canada’s COVID-19 new case curve looks virtually the same as the U.S., for the U.S. third wave, despite a vastly lower rate of vaccination in Canada compared to the U.S.)

My only point is that it’s plausible that we’re vaccinating fast enough to offset the growth of the (presumably) more-infectious U.K. variant.  The simple-minded comparison of the numbers was just too simple.  You can’t just take a couple of numbers (U.K. infectiousness, vaccination rate), put them side-by-side, and conclude anything.  But running those numbers through a simple equation to estimate the effective viral replication factor makes those magnitudes comparable and gives you the right comparison.  And when you do that, sure enough, the vaccination impact and the U.K. variant impact are in the same ballpark.

The math says yes, it might be a race between the U.K. variant and vaccination.  Of all the options on the table, that seems to be the most plausible explanation of the oddly stable situation in the U.S.  The U.K. variant is spreading like crazy.  We’re vaccinating 2M people a day.  And, on paper at least, it’s plausible that we’re seeing no particular change because those are offsetting effects.

If so, there’s no harm on projecting this out a bit.  I mean, seriously, if it’s a horse race ,who’d going to win?  In a month, 80% of new U.S. COVID-19 cases will be the U.K. variant or similar more-infectious variants.  (That’s from the simple model above).  And at 2M/day, we’ll have vaccinated another 18% of the U.S. population in a month, for which we have to net out the overlap with individuals already immune via infection.

Best guess, vaccination wins.  That’s how I’m calling it.  And it doesn’t win on its own.  It wins because its adding immune individuals on top of the large base of U.S. residents already immune via infection.  It wins because we’re close to herd immunity, and within that region, adding just a few immune individuals has a disproportionate impact on the spread of disease.

(Why?  Once you’ve reached (say) 50% of the population being immune to COVID, vaccinating another 10% reduces the still-susceptible half of the population by 20%.  Once you’ve reached 80% immune, another 10% vaccinated reduces the remaining susceptible population by 50%.  And it’s the still-susceptible population that is carrying on the changes on disease transmission.  The upshot is that a vaccination rate that is a steady fraction of the total population amounts to a rapidly-increasing fraction of the remaining susceptible population.)

In any case, for what it’s worth, based on my calculation, the spread of vaccination should beat the spread of the U.K. variant in the U.S.  We just have to avoid doing anything to increase risk for the next month or so.