Post #974: Today’s trend update, and maybe one more lesson from the French

Posted on January 25, 2021

Source:  Calculated from NY Times Github COVID data repository, data reported through 1/24/2021.

Just another boring post.  Thank goodness.

  • The COVID-19 new case rates continue to fall.
  • They are falling in more-or-less every state.
  • It’s not slowing down yet.  The case counts continue to fall at a constant percentage rate.  (It looks like it’s slowing down, above, because the thick blue line is starting to bend a bit.  But a graph like that doesn’t show the growth rate.  I’ll graph it on a log scale, below, to show the constant growth rate.)
  • It’s falling in more-or-less every state with more-or-less the exact same growth rate.  That’s a point that deserves further discussion.
  • Finally, Virginia’s curve now shows the predicted “speed bump” (Post #964).  The rate has begin to drop abruptly as the seven-day moving average passes the “lump” of cases reported circa 1/17/2021.

Log scale and constant growth rate.

I keep describing the current decline in COVID cases as weirdly coordinated across states.  Up to now, I’ve emphasized timing.  Let me now focus on the daily percentage rate of decline.

To do that, I need to start graphing the data on a logarithmic scale.  Instead of every hash mark on the graph’s Y-axis representing (e.g.) 10 more cases, every hash mark will represent 10 times as many cases.  Instead of 10-20-30 … for hash marks, you’ll have 1-10-100 … for the hash marks.

The joy of this seemingly otherwise useless exercise in math is that constant growth rates show up as straight lines on a log scale.  As illustrated above, where I’ve constructed the data to fall a constant 5% per time period.  That’s two graphs show the same data, graphed as reported (e.g., COVID cases) and graphed in log units (log of COVID cases).  The log graph makes the constant rate of growth appear as a straight line.

So, let me now focus on the rate of decline, in logs.

Here’s the same data as in the graph at the top of the post, where the Y-axis is a log scale.  Note that, to a very close approximation, the declining portion of the curve is now a straight line.

But that’s a) hard to see, really, and b) doesn’t really tell the full story.

So here’s another view of the nation, this time showing the individual states.  You’ve seen this graph here before. (I note in passing that you can clearly see the “speed bump” as Virgina’s rate now falls abruptly, as the moving average has now passed the bulk of the lump of cases reported circa 1/17/2021.)


Let me now take that exact graph, and focus on the decline by starting it at 1/1/2021, instead of 10/1/2020.  So this next one is the same data as above, just focusing in on January 2021.


OK, above, while all the states show decline rates, the lines appear to be converging, right?  The average “spread” of the lines, at the peak, is larger than at the right side of the graph.  So it looks like the high-rate states are falling faster than the low-rate states, compressing the lines together.  And that’s true, in terms of the raw case count.

But that’s NOT true, in terms of the daily percentage decline.  To see that, the graph below is the same data on a log scale.  Look at how nice, straight, and parallel most of those lines are.  The spread of the lines, at the peak, is more or less the same as the spread of the lines at the right edge of the graph.  Not only have most states exhibited a reasonably constant rate of decline, they’ve all exhibited more-or-less the same constant rate of decline. 

I keep characterizing the decline as weirdly uniform.  First in terms of timing.  And now in terms of rate of decline.  It’s hard for me to believe that this is purely by chance.  I have to believe there’s some sort of causative agent behind this.  But damned if I can figure out what it is.

I will note, however, that I believe this is how a classic, simple model of an epidemic should behave.  If some unknown force suddenly reduces the rate of COVID transmission (dropping the “R-value” so that each person now infects fewer than one additional person) you should see a slow, roughly constant decline in the new case counts.  Only as you approach herd immunity will that rate of decline speed up, resulting in an acceleration of the decline as you approach zero new cases.

At least, that’s my crude understanding of the dynamics of it.  I’m still in the process of writing up a post on all the things I still don’t understand about the simple arithmetic of herd immunity.

But speaking of the French …

But what about the French?  Harking back to the last post, the thing that finally  turned the French off to vaccines was their federal government wasting large sums of money.   That occurred during the H1N1 epidemic of 2009.  (Per this article in The Guardian).  In hindsight, the French government ended up wasting something like a third of a billion Euros on vaccine that was never used.

I just thought that was something for the new majority party to keep in mind, as we look at the current case trend and get ready to borrow our next couple of trillion dollars to deal with COVID-19.  Because that’s not for dealing with COVID as it exists now.  That’s going to be spent dealing with COVID as it exists some months from now.

And if any of that appears to be wasteful, you can bet they’ll be criticized for it.

Right now, using the system ginned up by the CDC under Trump, we’re managing to get about 1M persons/day vaccinated.  (Per this Washington Post article, and evident to anyone who’s been tracking the CDC vaccine counts.)  The Biden-proposed 100M/100 days just continues the existing rate.  (And, apparently, that’s more-or-less all the vaccine that manufacturers appear able to deliver over that period anyway).

Despite that, there are plans in the works for 100 new federally-run mass immunization sites.  Aside from my distrust of eye-candy round numbers (100M, 100 days, 100 sites — cut me a break, already), you have wonder how well that was thought-through, relative to a more normal method of vaccine distribution (Post #968).   Was there some sober, cold-eyed needs assessment?  Or did the decision-making go no deeper than “nice-looking round number”?  Which is pretty much how it appears.

Recall from Post #968, the US routinely does 100M flu vaccines in 60 days without batting an eye.  In a normal year.  Using normal distribution channels.  No lines, no waiting.  I wonder how this unique effort dovetails with the existing distribution channels, if at all.

Sure, the U.K. variant is lurking in the background.  And that variant almost guarantees a fourth wave, if we’re lucky enough to be at the end of the third wave now.  But by that time, if we’re down to the point where we allow Joe and Jane Citizen to be vaccinated, that can be done using routine methods, I think.

I’ve actually read through the President’s plan (.pdf).  And while it does in fact describe what they are going to do, there’s  not a lot of numbers to back that up.  Projections of likely disease incidence, and so on.  It’s comprehensive, it touches all bases, but after reading it, I had to ask how much was just pure zeal, and how much was rational analysis.

(Example:  They’ve proposed to use the Defense Production Act to produce PPE.  Due to a presumed shortage.  Which is a nice sentiment, but it’s only a sentiment.  No estimate of how much of a “shortage” there is, or how they would define “shortage”.  Not even a rough guess as to how much PPE they plan to command to have produced, in this fashion.  E.g., how many N95 masks they will command into production, above current levels.  And so on.  Lot of words.  Not a lot of numbers.)

I guess we’ll find out.  In today’s political climate, if they overshoot the response, it’s a sure bet they’ll be castigated for it.

Personally, I’m not slacking off.  Just yesterday I fired up my second humidifier, as the relative humidity in my home fell below 40% (Post #894) in response to the recent cold snap in Virginia. I’m minimizing my trips to public areas, and I’m continuing to wear an N95 respirator as I shop.

And I’ve already asked and answered the key question:  If my vaccine dose gets here after the pandemic is over, I’m still going to take it (Post #959).  That seems like an odd thing to say, in the current context.  Let’s all hope it seems a lot less odd, when the time comes for me to get vaccinated.