A faster rate of decline
We’re now more than three weeks past the peak of the U.S. fourth wave, which I date to 4/14/2021. And an odd thing seems to be happening. The rate of decline in new cases per day seems to be speeding up.
That’s shown in the inset table below. For the U.S. as a whole, and for most of the regions, the rate of decline sped up after 5/1/2021.
Source for this and all other graphs of new cases: Calculated from The New York Times. (2021). Coronavirus (Covid-19) Data in the United States. Retrieved 5/7/2021. https://github.com/nytimes/covid-19-data. The NY Times U.S. tracking page can be found at https://www.nytimes.com/interactive/2020/us/coronavirus-us-cases.html.
That doesn’t look like much, and it might just be temporary. But the interesting thing is that the conventional wisdom regarding epidemics says that shouldn’t happen.
Conventionally, when an epidemic dies out of its own accord — from the immunity of people who have survived an infection — the rate of new infections slowly winds down. That happens due to a natural negative feedback, in that the number of newly-immune individuals tapers off as the rate of new infections tapers off.
As I have pointed out before, that classical epidemiological model does not apply here. The main source of new immunity isn’t people who’ve survived infections. It’s people who have been vaccinated. And there is no necessary relationship between the rate of new infections and the rate of vaccination. If we were smart enough, the rate of vaccination could remain constant right up to the end of this pandemic.
Unfortunately, it’s increasingly clear that we aren’t that smart. We’re now down to about 2 million vaccine doses per day, down from a peak of about 3.5 million per day.
Source: US CDC COVID-19 data tracker.
That said, we continue to make progress on achieving herd immunity. The bottom-line number on the table below ticked up by one percentage point since 5/1/2021. The calculation in the table below includes both individuals who are immune via prior infection, and individuals who have been vaccinated. It embodies a lot of assumptions, the most important of which is that there are four un-diagnosed COVID-19 infections for every diagnosed infection. (You can see a full sensitivity analysis for this table in Post #1131).
Whatever you may think of the underlying assumptions, this method is certainly superior to assessing herd immunity by counting vaccinated individuals only. Pretty much all popular press coverage of the herd immunity issue is based on that. And that’s led to the pessimistic assessment that we’ll never get to herd immunity. While this, by contrast, includes an estimate of those immune via infection or vaccination, and provides a much more realistic (and optimistic) assessment of where we stand regarding herd immunity.
Coherent trends within regions, outliers regress toward the mean.
A second interesting aspect of the current situation is that there’s starting to be a lot of coherence in those regional trends. They aren’t being driven by a single state, but by uniform changes across all the states.
A few picture are worth a thousand words.
Below is the U.S. East Coast, the Northeast and South Atlantic regions.
Even where there isn’t much regional trend, that’s not because the individual states are moving in different directions. That’s because most of the states show no trend. Here’s the Midwest, South Central, and Mountain regions:
It’s also worth nothing that the big outliers — Michigan and Minnesota, in the Midwest, and Colorado, in the Mountain area — are now moving back toward the average. That is, all the outlier/outbreak states appear to have peaked.
The only exception to “coherent trends” is the Pacific region, which includes the U.S. West Coast plus Alaska and Hawaii. Even there, the last two states with strong upward trends — Oregon and Washington — now appear to have peaked.
In summary, even if you look in detail, it’s hard to find anything bad within the current trends in COVID-19 cases in the U.S. No outbreaks, no states with long-standing unbroken upward trends. Not much of anything, really. Just an accelerating downward trend in most areas.
Some COVID-19 free areas? A deeper dive to the county level data.
A week ago (Post #1131), I flagged all the counties of population 5,000 or more that had seen literally zero COVID-19 cases for the prior four weeks.
Obviously, given how small those counties are, this might occur purely by chance. So the “COVID-19-free” nature of those might be an illusion. COVID-19 could be circulating, and I just happened to observe them during a particularly good four-week stretch.
On the other hand, maybe sparsely-populated rural areas have an advantage in terms of “extinguishing” COVID-19.
In any case, the question is, what does the list above look like, if I move forward by one week?
The answer is that it’s quite persistent. Of the five counties identified last week, four remained COVID-19 free for another week. Thus, the list above is actually a list of counties that have been COVID-19 free for at least the past five weeks.
For three reasons, I think this is a real phenomenon, and not merely a statistical fluke.
First, of the roughly 400 U.S. counties with 5000 to 10000 population, only 10% of them will have zero COVID-19 cases in any given week. Thus, if this were merely by chance, the likelihood of observing five weeks in a row for any one county is 0.1^5, or 0.00001. With a pool of 400 counties, if this were purely random, the likelihood of seeing even one county being COVID-19 free for five straight weeks is about 0.4%.
Second, they are geographically clustered. There are small counties all over the U.S. But Kansas has a very high concentration of those low-population COVID-19-free counties. Here are all the Kansas counties that have had zero reported COVID-19 cases in the past five weeks, regardless of population.
Finally, there is some reason to think that isolated rural areas would be the first to extinguish COVID-19 entirely. That’s due to the outbreak threshold effect, as explained in this scholarly article. I went through that thoroughly in Post #1003. The bottom line is that, for something like COVID-19, if you have fewer than five active cases in an isolated population, the odds are that the chains of infection will simply die out, due, in effect, to bad luck. That’s from the graph below, for R-nought of 3, from applied to the curve for the previous SARS epidemic.
N.B. “Log” above is natural (base e) log.
And so, tentatively at least, I’m beginning to think that there are some small, isolated rural counties that may, in fact, be COVID-19 free. I think that’s worth keeping an eye on, to see how that progresses as the overall average rate of new COVID-19 cases continues to fall.
