Post #1127: COVID-19 trends to 4/28/2021, and a NY Times article on the end of the pandemic that gets the math wrong.

Posted on April 29, 2021

Trend?  No change.  The U.S. average daily new COVID-19 cases per 100,000 continues to fall slowly.  It’s falling in most regions.  There’s no new crisis area to take the place of Michigan.

But don’t confuse slow change with no change.  New case rates are now down almost one-quarter since the peak of the U.S. fourth wave.

Some perspective.

Instead of focusing on the small and stable downward trend, let me try to get some broader perspective.  Mainly, will this damned pandemic ever end?  And if so, how?

First, the pandemic is now confined to an increasingly small portion of the population.  Plausibly, more than two-thirds of the population has full immunity to COVID-19 now.

Source:  CDC

More than half of U.S. adults have some vaccination.  The data on “breakthrough” infections (infection after vaccination) shows that COVID-19 infections in this population is incredibly rare.

Source:  Calculated, with significant assumptions, based on data from the US CDC.

To that vaccinated population, we have to add all unvaccinated individuals who have recovered from a COVID-19 infection.  Again, re-infections in that population are rare.  The upshot is that the new COVID-19 cases we are seeing, right now, plausibly come from less than one-third of the U.S. population.

Another way of saying that is the potential COVID-19 carriers are getting more spread out within the population.  At some point, assuming that anything about epidemiology is true, they will get thinly spread enough that the pandemic will finally fizzle out.  Enough chains of disease transmission will be stopped, by running into immune individuals, that the circulating level of COVID-19 should drop to something negligible.

An incorrect analysis in the NY Times.

I just read a NY Times article claiming that the pandemic will end though the slow process of “exponential decay”.  This was headlined as an exercise in math, but it was in fact presented without any actual math.

The case presented in the NY Times is what you may read in textbooks.  Epidemics end with a slow tapering-off of cases.  As the number of new infections slows, the additions to the pool of immune individuals slows in direct proportion, and that feedback loop means that the epidemic just gradually and slowly fades away.

But I think that’s dead wrong in the current situation.  It simply fails to account for a pandemic occurring in the middle of massive drive to vaccinate the population.  The number of newly immune cases now has almost nothing to do with the infection rate.  As I show below, that’s now driven overwhelmingly by the vaccination rate.  To a close approximation, the number of newly immune cases per week is a constant, and could remain so right on up to the end of the pandemic.

Let me just put the numbers down here, so you can see that.  Here’s my “herd immunity” chart from about a week ago.  Compare it to the one presented earlier and you will find that, of the 5.6 million newly-immune persons, roughly one-quarter came from new infections, and three-quarters came from new vaccinations.  (And that’s with my somewhat-aggressive assumption that there are still five total COVID-19 cases for every diagnosed case, as well as an assumption about overlap of vaccinated versus recovered immune individuals that may no longer hold true for additional infections versus additional vaccinations.)

And so, the main driver of the newly-immune pool is not those who’ve been newly infected.  The main driver is vaccinations, and that has nothing to do with the infection rate.   To be crystal clear, there’s no mathematical linkage between that, and the infection rate.  We could easily have a new-vaccination rate that holds steady from now to the very end of the pandemic.

You get that slow “exponential decay” if and only if the additions to the immune population come solely from those who survive infection.  That gives you the negative feedback that slows the rate of decline.  By contrast, if that pool of newly-immune is actually driven by some constant rate of new vaccinations, then you ought to get a fairly abrupt end of the pandemic.  As long as the vaccination rate holds up, you should see a more-than-exponential decrease in the rate of new infections.

Even though the pandemic appears to be fizzling out, that’s not what the math says should happen.  Not when the end is being driven by a constant number of newly-vaccinated individuals per day.

Best guess, the only reason we haven’t seen that abrupt decline is the spread of the more-infectious U.K. variant B.1.1.7.  Near as I can tell, what we’ve seen for the past few weeks is a race between vaccination/herd immunity and that variant (see statistical analysis Post #1101).  Vaccination appears to be winning.  And when I do the math, the math says that if we can just keep this rate of vaccination up, this isn’t going to fade away.  This should end rapidly and decisively.  If people will just have the good sense to get vaccinated.

And so, I’m sticking with what I said three months ago, Post #894.  Once you add a high rate of vaccination to the picture, you shouldn’t see slow, exponential decay.  The math says that you ought to see a rapid and decisive end.