Post #1160: COVID-19 Delta variant bodes for a 5th U.S. COVID-19 wave

Posted on June 15, 2021


If you can’t beat ’em, rename ’em.

If you track trends in COVID-19, you’re probably well aware that a new variant has taken over Great Britain and is in the process of taking over the U.S.  This is the COVID-19 variant formerly known as “Indian”, B.1.617.2.  Henceforth to be called Delta.  The British variant is now Alpha.

In this post, I’m getting my thinking straight about the new Delta variant.  Best guess is that, as with Great Britain, we’re going to get another wave of increased daily new case counts from the spread of the Delta variant.

Delta makes herd immunity effectively impossible with current vaccines alone.

I’m fairly sure this cheery bit of new is correct.  I’m almost equally sure you aren’t going to see anyone in our public health establishment saying it in public.  But math is math, and this new variant brings a double whammy.

  • The virus is more contagious
  • The vaccine is less effective

Practically speaking, those two factors put herd immunity via vaccination out of reach for the U.S.

Briefly recall how this works.  A pandemic will eventually collapse if each infected individual goes on to infect an average of less than one new individual.  If you can get that to happen, each round of newly-infected individuals is smaller than the last, and the pandemic shrinks away.

Now recall “R-nought” and the classical definition of herd immunity.  R-nought is the number of individuals each infected person would go on to infect, if there were no protection or immunity within the population.  For example, if each infected person would normally go on to infect three others (R-nought of 3.0), you need to interrupt at least two-thirds of those infections to bring the pandemic to a halt.  If R-nought is 10, you’d need to interrupt 90% of those infections to bring the pandemic under control.  And so on.

The more infectious the virus, the more people need to be immune to it before you achieve herd immunity.  Or the more COVID-19 hygiene protocols need to be enforced to cut off what would otherwise be chains of infection.

(I need to put a marker down here.  Epidemiologists always discuss this solely in terms of preventing new infections via vaccination.  But prior infections also confer immunity.  And good COVID-19 hygiene also prevents infections.  In reality, all of those factors work to interrupt would would otherwise be chains of disease transmission, and so all of those factors matter in a herd immunity calculation.  But for the rest of this section, I’m going to do what all the epidemiologists do, and pretend that the only way to interrupt chains of infection is via vaccination.)

The first key fact is that the Delta variant is more infectious than the Alpha variant which is more infectious than the original strain.  Rather than try to daisy-chain all those imprecise numbers, I’m just going to take somebody’s estimate.  Like so, from this seemingly-plausible reference, where R0 = “R-nought”:

Professor Cheng said last year's Wuhan strain had an R0 value of around 2.5, the Alpha strain was about 3.75 and the Delta strain was about 5.

That means if we were living life like we were in 2019, one person with the Delta strain would likely infect five other people, compared to just 2.5 last year.

I’m sure there’s considerable uncertainty around that estimated R-nought of 5.0 for the Delta variant, but I’m just going to accept it as a fact.  (You can find apparently legitimate sources suggesting a much higher value.)  And so, if each each infected individuals would natively infect 5 others, you have to interrupt four out of five of those infections to bring the pandemic under control.  In other words, with the estimated R-nought of 5.0 for the Delta variant, we now need to have 80% of the U.S. population immune to it before we have any hope of it going away.

The second key fact is that the vaccines are less effective against this strain of COVID-19.  The Pfizer vaccine is 88% effective against the Delta variant after two shots.  But, for the U.S., nobody knows how effective the Moderna or Johnson and Johnson vaccines will be.  Fauci guessed that Moderna will be about as effective as Pfizer, but that’s just a guess.  The AstraZeneca vaccine, commonly used in Great Britain, is only 60% effective against the Delta variant.  (The Pfizer and AstraZeneca numbers are based on this study.)

If vaccination were the only way to stop this, between those two factors, we would require at least 91% of the U.S. population to be vaccinated before we could achieve herd immunity.  (That is, .91 x .88 = .80, the level of immunity required for herd immunity against the Delta variant.   Re-stated, 91 percent of the population, vaccinated with an 88% effective vaccine, would stop 80 percent of the chains of infection.)

Short of vaccination-at-gunpoint, that’s not going to happen.

(There are some nuances here.  Probably, you are less likely to transmit the disease, if infected, if you are vaccinated.  And people will continue to achieve immunity by recovering from infection.  But in terms of your textbook herd immunity calculation, herd immunity is pretty clearly out of reach for the U.S. population.)

In practice, two things happen when you try to calculate where we stand on herd immunity with the Delta variant.  First, your estimate of the existing level of immunity falls, because the existing vaccinated population has less immunity to this new strain than it did to the existing strain.  And then, separately, the fraction of the population that needs to be immune goes up.

Again, between those two factors, there’s a world of difference between the way the U.S. looked against the Alpha (British) variant, and how it now looks against the rapidly-spreading Delta (Indian) variant.

Let me now redo my herd immunity chart.  This still assumes that you have complete immunity once you’ve recovered from infection.  I’m not changing that for now.  I’m only changing how effective one and two vaccine shots are.

Alpha variant (what we have now, the British variant).

  • R-nought = 3.75
  • Herd immunity goal = 73% immune
  • Current estimate = 64% immune.
  • Additional full vaccinations required = 9.5% @ 95% effectiveness

Delta variant (what is coming, Indian variant).

  • R-nought = 5.0
  • Herd immunity goal = 80% immune
  • Current estimate = 59% immune.
  • Additional full vaccinations required = 24% @ 88% effectiveness

As I said, double whammy.  We need more immunity to achieve herd immunity, and we instantly have less immunity, because the existing vaccinated population has less resistance to this new strain.

Where do we stand on the Delta variant and its growth

Let me first quickly benchmark Great Britain’s latest outbreak.  Currently, the Delta variant accounts for almost all (90 to 94 percent) of new cases in Great Britain.  At about 7000 new cases per day in a population of 66 million, that’s about 10 new cases / 100,000/day, with a strong upward trend.  And that’s despite significant restrictions on public life and public gatherings in Great Britain.

That compares to the current U.S. rate of about 4 new cases/ 100,000 per day.  And a slight downward trend.  With, as far as I can see, roughly no restrictions on public life left in most U.S. states.

The vaccination situation in Great Britain is roughly comparable to that of the U.S.  Fully-vaccinated individuals in Great Britain account for about one percentage point more than in the U.S., and Great Britain has injected about 14% more total doses per capita.  But a) a large share of their vaccinations are the AstraZeneca vaccine, which is less effective than Pfizer against the Delta variant, and b) those with just a single shot of vaccine receive little protection against the Delta variant (one shot of vaccine is about 33% effective).

The U.S. has the edge in terms of total reported cases per capita so far.  Presumably, those individuals add to the pool of persons immune to COVID-19. In the U.S., over 10 percent of the population has been diagnosed with COVID-19, versus about 7 percent of the population of Great Britain.  For each diagnosed person, there is probably another 2 to 3 persons who had COVID-19 but were not diagnosed.  (All of those statistics would depend strongly on test availability and testing behavior.).  Thus, the U.S. plausibly has an additional 10 percent of the population immune via recovery from infection, compared to Great Britain.

(FWIW, I looked up all of those statistics, I’m just too lazy to provide citation as to source for every one of them, as they are just background.)

What fraction of new cases is accounted for by the Delta variant in the U.S.?  This is a number that is changing rapidly, so you need to pay strict attention to the dates.

As of the two-week period ending 6/5/2021, the CDC estimated that the Delta variant accounted for just under 10% of all new cases in the U.S.

Source:  CDC COVID data tracker.

The doubling time for these cases in the U.S. appears to be something less than two weeks.  (The last three sets of CDC two-week observations or projections were 1.2%, 2.5%, and 9.9% of new cases.  In each two-week period, the fraction of new cases attributed to Delta more than doubled.)

Without bothering to define it, the case-weighted midpoint date for that two-week period ending 6/5/2021 is about 5/31/2021.  (The 9.9% is the average for the entire period.  It was less than that early on, greater than that later.  The date of  5/31/2021 is my best guess for the day, over that period, when the fraction literally hit 9.9%.)  That was more than two weeks ago.  Hence, we should add just over two weeks’ growth to that estimate to project forward to the rate as of 6/15/2021.  So, something in excess of a  doubling of those cases.

Best guess, by that calculation, somewhere around one-quarter of new US COVID-19 cases on 6/15/2021 were the Delta variant.  At that rate, it should be the most common strain of the virus in the U.S. by the end of this month.

Is it different this time?

The U.S. fourth wave was due to the growth of the British (now Alpha) variant, moderated by the rapid increase in vaccination.  It was a race, and back in early March (Post #1051), I used the best available data to project that vaccination would win.

I emphasize that to demonstrate that I’m not some nervous Nellie who cries “wolf” at any pretext.  The numbers reasonably clearly indicated that at the then-prevalent rate of new vaccinations, and the known efficacy of the vaccine, we’d be able to vaccinate enough individuals to stifle a major outbreak of the British (Alpha) variant.

But now?  Now we’re bringing in a variant that is yet-again as infections relative to Alpha, as Alpha was to the original COVID-19 variant.  But now,

a)  There’s no big build-up of vaccinations to offset that.  To the contrary, the U.S. vaccination rate is down to 1M per day.

Source:  CDC COVID data tracker.

b)  We’re dropped the greater portion of our COVID-19 hygiene at the CDC’s direction.

c) Good luck getting people to mask up again in case this gets ugly.  What are the odds that the CDC will be able to pull a timely about-face and tell us to put our masks back on, and then have Republican governors follow that advice, let along the U.S. population as a whole?

and finally,

d) The lower efficacy of the vaccine against this strain means that, from the outset, we lose ground as this variant spreads.  To be clear, not only is vaccination not rapidly increasing our collective immunity, instead, the lower efficacy of the vaccine means that we are, in effect, losing immunity.  That was the whole point of the charts in the second section above.

The way I see it, at this point, this time, whatever happens, happens.  Certainly no Republican states, and likely no states, are going to take action in the event that the Delta strain leads to a U.S. fifth wave.  So whatever is going to happen is going to happen.

Run that mix through the blender and my guess is that we’re going to have (some sort of) a fifth wave.  Not, as I initially expected, due to heavy use of air conditioning mid-summer, as was the case for the U.S. second wave.  But because we’re facing yet another round of substantial increase in the infectiousness of COVID-19, and far from taking offsetting measures, we’ve all let our guards down and are vaccinating at a casual pace.

On the plus side, at some point, the virus runs out of bodies.   We now have a fairly large chunk of the population that is immune.  So this can’t possibly be as bad as the U.S. third wave.   But my bet is, this pandemic isn’t over yet.   Just as it is not yet over in Great Britain.