Source: Calculated from NY Times Github COVID data repository, data reported through 2/2/2021.
Just a brief reminder, because this gets next-to-no news coverage.
Peak-of-the-peak occurred 1/8/2021: Rounded, that was 78 new cases / 100,000 / day (seven day moving average).
Currently, as of 2/2/2021: Rounded, it’s 44, ditto. Or a 44% reduction in new cases/ 100,000/ day.
I’m not alone in my thinking, but I’m not seeing empirical confirmation.
I’d now like to direct your attention to an article published on 1/8/2021, or literally the day of the peak. In it, a former FDA Commissioner predicted that incidence (new cases) of COVID would begin to fall, due to the increasing proportion of the population that is immune, either from infection or vaccination. Aside from applauding his sense of timing, it’s somebody with bona fides saying more-or-less exactly what I’ve been saying here.
What I’m still hoping to see, but haven’t seen yet, is the negative growth rate begin to accelerate. That would show up on the log graph above as a steeper slope on that blue line. The idea being that the buildup of immune individuals — via infection and vaccination — will result in a reduction in the viral replication factor. And so, a faster descent down that blue line.
Without vaccination, that end-phase of the pandemic wave happens only slowly, as the reduction in new infections slows down the whole feedback loop. You get fewer and fewer people added to the immune pool with each passing week, as the new infection rate drops.
But vaccination continues to drive that immune pool up, even as the slowdown in new cases reduces newly-immune-via-infection. So with vaccination, not only does this “virtuous circle” show up, but you ought to be able to see the drop in the new infection rate appear pretty quickly.
How quickly is quickly, exactly?
Well, at present, maybe another half-percent of the population, per day, is now (on the path to) acquiring immunity. I get that from comparing older and newer versions of my “herd immunity” spreadsheet. So that counts each half-vaccinated person as half-immune, but counts them immediately, despite the fact that it takes considerable time for antibodies to develop. (There are also some un-accounted-for trends (new cases are falling, new vaccinations are rising), but I didn’t feel like trying to project those forward.)
Below is 1/21/2021 and 2/1/2021.
And then, as noted in an earlier post, any effect of that, on infection rates, will show up in the data 16 to 25 days later. So there’s this slow shift in the population, which should show up only after a couple of weeks of lag time.
Weirdly enough, it’s just a matter of algebra to translate that growth of the immune population directly into an expected impact on the viral replication factor and so on the projected growth rate. But you have to assume away any sort of self-selection. (You have to assume that the newly infected and newly vaccinated populations are representative of the U.S. population as a whole — which they are not.) And you further have to assume that all the factors preventing viral transmission add up to the cannonical “70%”, as I discussed at length in a series of posts last week.
You also have to get just a little more sophisticated than my simple presentation of last week. You have to break the U.S. into two populations — immune and non-immune — and work out the numbers that way, instead of pooling them all together as I did in my prior analysis.
Let’s assume we’re currently somewhere around the situation shown in this equation below, with a viral replication factor of .9 (10% reduction in cases per estimated 4.5 day viral replication cycle).
To get to the actual, observed 0.9 replication factor, we start from the original unconstrained viral replication factor (R-nought) of maybe 3.33. Then you subtract out all the immune people, and some proportion of the non-immune people. That’s saying that immunity prevents 100% of infection, and that COVID hygiene prevents some fraction of infection, that would otherwise have occurred.
- 3.33 * (1 – I% –b*NI%) = .90 (viral replication factor)
- I = immune
- NI = not immune
- b is the protective effect of masking, social distancing, and such.
By way of explanation, this assumes that every immune person is completely immune, and so those people break up the viral transmission events one-for-one. (So the implied coefficient on I% is 1.0). And that COVID hygiene (masking, etc.) breaks up some fraction of viral transmissions in the non-immune population, where b is that fraction.
Plug in the current data and solve for b. Currently, 43% immune, by my estimate.
- 3.33 * (1 -.43 – b*.57) = .90
- Solving, b ~0.53
- 3.33*(1 – .43 – .53*.57) = .90
And so, as I found with my prior attempt at applying algebra to this, the .53 coefficient means that the effect of masking/distancing, and so on was to cut the viral transmissions in half. It’s effectively the same as having immunized half the population.
Now boost the immune population by one week’s growth, or 3.5%.
- 3.33*(1 – .465 – .53*.535) = .84
You drop the viral replication by 0.06. Translate those into weekly rates of decline:
- .90 ^ (7/4.5) = .85 (or 15%/week average decline in new cases).
- .84 ^ (7/4.5) = .76 (or 24%/week average decline in new cases).
Two weeks growth in the immune population? Ought to see a 32% per week decline in the new case count. And so on.
See what I’m trying to get at? If we’re right at the edge of controlling this, force-feeding just a week’s worth of new immune individuals into the system should have a large impact on the growth rate. Easily large enough to be visible on the graph. And the weekly rate of decline should continue to accelerate.
There are a lot of assumptions in this analysis, but I think the general conclusion is fairly robust. We ought to be seeing a visible and steep acceleration in the decline in new cases.
No joy yet.
Only problem is, we’re not seeing that. Either I’m wrong about the current state of the pandemic, or it’s just taking a lot longer than anticipated for this effect to show up.
One possible error is that I’ve assumed that no infected individuals are losing immunity, at this point. I think that’s a reasonable assumption, given that the bulk of infections occurred in this second wave. But at some point, I need to stop counting the persons who were infected very early on, because the science says that at some point, they’ll likely lose immunity to COVID. As of now, taking six months as a conservative estimate for retaining immunity, dropping the oldest infections would have only a modest impact on my count of immune individuals. I don’t think that would materially change the conclusion.
A second possible source of error is that maybe much of the vaccinated population wasn’t likely to spread the disease anyway. Maybe it is strongly self-selected for a combination of individuals that already take significant precautions (health care workers, for example), and those who have been and will continue to be sheltering well (elderly, younger persons with conditions that raise risk of severe COVID). If that’s true, then vaccination isn’t drawing down the population of people likely to spread the disease. And the net effect of vaccination so far is far less than the one-for-one reduction that I’ve assumed. (Every percentage point added to the immune population came out of the still-at-risk non-immune population).
A third explanation is leprechauns. Or, as it would be termed in this case, “seasonality”. That is, some absolutely unobservable factor that simply causes the viral replication factor to fall, for no apparent reason. And as it falls — everywhere, all across the U.S. — then the new-case rates decline. For no reason.
That’s obviously an unsatisfactory explanation, because it’s no explanation at all. “Seasonality did it” is more-or-less indistinguishable from “leprechauns did it”. Plus or minus a pot of gold here or there. It’s not really an explanation at all.
Or maybe this is just totally off-base. But, really, it’s just the basic, accepted textbook arithmetic of pandemics. And, per the cite above, you’ve got a former FDA Commissioner pretty much pointing out exactly what I’ve been pointing out. Maybe the textbook model is just too simple to capture actual behavior.
And so, I continue to wait for a sharp downward bend in that blue line above. The numbers are what they are. If this doesn’t happen, then I’m wrong. In which case, I’m blaming the leprechauns.
And with the mythical post-holiday surges, at this point, every day that it doesn’t appear makes it less likely that we’re ever going to see it.