Source: Calculated from NY Times Github COVID data repository, data through 2/9/2021.
Just a quick recap of what I’m waiting to see in the data, and why. And why the recent sharp decline in new case growth in North Dakota might or might not be it.
What am I expecting to see? I’m looking for an increasing rate of decline in new cases. And that should end with a nose-dive in new cases. In other words, the end of this wave shouldn’t just peter out, it should accelerate to a finish.
Why do I expect to see that? It’s just arithmetic. As you build up the number of people who are immune, the population of disease carriers gets smaller and smaller. At some point, every percentage point of the population that gets immunized takes a bigger and bigger chunk out of the remaining disease carriers.
In the textbook model of an epidemic, you always see the end of the epidemic pictured as a slow tapering-off of new cases. And that’s true if the epidemic ends of its own accord, that is, fizzles out as enough people gain immunity via infection. In that scenario, as the new-infection rate tapers off, you feed fewer and fewer newly-immune people into the system. So things slowly grind to a halt.
Here, by contrast, a high rate of vaccinations feeds a constant stream of newly-immune people into the system. By force-feeding the pandemic this stream of immune people, you prevent the rate of decline from slowly tapering off. What you ought to see, in the end, is a rapid decline.
Where am I expecting to see it first? All other things equal (e.g., COVID hygiene practices), I ought to see this first in the state that has the highest fraction of the population immune via a combination of infection and vaccination. This is why I keep perseverating on North Dakota. Practically speaking, absent any other information, that’s where I ought to see that first. Followed by a handful of Midwest and Mountain states that had exceptional COVID outbreaks at the end of 2020.
What’s the holdup? There are five real-world details that complicate this nice, neat story.
- It takes six weeks to develop full immunity after your first vaccine shot. So we really need to lag the vaccine counts by something like six weeks. Then add them into the count of immune persons.
- They’re vaccinating everyone, including those who’ve already recovered from COVID. So the number of newly immune people is only a portion of the newly vaccinated due to the overlap of the already-infected and already-vaccinated populations.
- We’re focusing vaccination on people who aren’t out-and-about. Right now, this is mostly a pandemic of working-age adults. They are out-and-about, and they have the highest incidence of new COVID cases. But our vaccination rules favor, among others, nursing home residents and those 65+. Those individuals are at risk of severe COVID, but aren’t the ones out in the community spreading COVID. And so, they aren’t going to be out there preventing the spread of COVID, once they are immune. This reduces the impact of vaccination on blocking transmission (see my post about Grandma and the Superbowl).
- It’s not clear that vaccination prevents you from getting infected (and so being able to spread disease). The only thing that was tested was the extent to which vaccine prevents symptomatic, severe COVID. The extent to which it prevents mild and asymptomatic cases is unknown. (But the presumption is, I think, that if the vaccinated population can still spread disease, it will be far less effective at it, given the lower severity of infections post-vaccination.)
- You eventually run out of people who are willing to get vaccinated. So the notion that vaccines continue apace until everybody gets their shot is unrealistic.
- (Belatedly, I forgot to mention reporting lags and recovery lags. The persons-infected number is reported 12 to 21 days after the infection event, it takes some time for the infected person to develop immunity, and then we look at a seven-day moving average of infections. The effect of all of that is more-or-less to smear the data over time.)
What will it look like, when you see it? I’ve been hoping it would look about like what you see below. The data source for all three graphs below is the NY Times Github data repository, data reported through 2/9/2021.
The first graph is all states, starting 1/1/2021, graphed in logs (so constant growth graphs as a straight line.
The second graph is just the Midwest, but starting 10/1/2020. Again, in logs, to show constant growth as a straight line. This emphasizes the extent to which North Dakota has broken from the pack.
Below, same graph, natural units, not nearly as impressive, but still visible:
I’m not fully convinced that what we’re seeing in North Dakota really is the end-game of herd immunity. But it might be.
I laid out the arithmetic on this a couple of weeks ago (Post #894). And I’ve been harping on ND and herd immunity for the better part of two months now. As data analysis goes, that’s about as good as it gets: I’m seeing what I expected to see, where I expected to see it. And I’m not seeing it, where I didn’t expect to see it.
What gives me pause is that there was no gradual transition to a faster rate of decline. Basically, North Dakota’s rate of decline matched that of the rest of the Midwest up to maybe five days ago. And then, all at once, it diverged. There’s no justification for that based on the simple arithmetic of a pandemic.
Now let me gin up one last table, showing an estimate of combined total infections and immunizations by state. Because, obviously, what I’d like to see is another few states do what North Dakota just did, and have their new case growth take a sharp downward turn. And I’d really like to see those states cluster near the top of the next table.
This clearly involves a lot of assumptions and approximations. (It assumes that the ratio of total infections to diagnosed infections is a uniform 5:1 in all states; it assumes that ratio has been constant across all U.S. waves of the pandemic; it assumes that the overlap of the vaccinated and infected populations is random and uniform in all states; it assumes that prior infection confers complete immunity and that immunity has not yet faded for the early-infectees.)
And this table does not account for variations in COVID hygiene, such as propensity to wear a mask, to attend mass gatherings, or to eat and drink in restaurants and bars. Variations in COVID hygiene will affect the extent of disease spread, and so affect the point at which the pandemic begins the rapid wind-down in each state.
That said, if ND is in its final nose-dive of the current phase of the pandemic, then the next state to follow suit ought to be near the top of this list. Plus or minus all the caveats above.
There is one further caveat on the vaccine data. Not all vaccine doses are tracked by state. In particular, just over 5% of all administered doses have been delivered via four Federal agencies: Department of Defense, Veterans’ Administration, Indian Health Service, and Bureau of Prisons. Those doses are not tracked to the individual states in which they were administered. In particular, this means that the state counts above will understate actual vaccine delivery in areas with (e.g.) a large number of Indian Health Service and Tribal health care facilities.
In summary: Something new is happening in North Dakota. The rate of decline in new cases/capita has suddenly increased, relative to the rest of the states. Sure, it’s just one state. But given how nicely uniform the picture looked before this, it’s pretty startling.
If this is the result of finally hitting “herd immunity”, we ought to see other states near the top of the listing above follow suit in the near future. So that’s the next thing to watch for.
