Source: Calculated from NY Times Github COVID data repository, data reported through 1/28/2021.

I’m going to do one more post on herd immunity and vaccination. But this is a very positive post. **The point is, vaccinations at the current rate should vastly speed up the end of the U.S. third wave of COVID. **

**That’s really not obvious, is it?** Conventional wisdom is that vaccinations will help us get this under control many months from now. But that conventional wisdom springs from a fundamental misunderstanding of herd immunity. It springs from the thoughtless repetition of “70% required for herd immunity”,without realizing that’s for herd immunity in isolation, *with no other COVID hygiene measures in place.*

By contrast, *as long as we continue masking/distancing/limiting, *infections alone have already brought us near or past the point of what I call “remission” herd immunity. (See e.g., Post #982). The fraction of the population that is immune via infection is roughly enough to drive the viral replication factor (R) below 1.0. Again, as long as we continue masking/distancing/limiting.

The implication is that newly-vaccinated individuals aren’t moving us slowly in the direction of some far-off target. They are moving us well past the level required to get viral replication below 1.0. Right now. And though the magic of leverage and compounded growth rates, every percent of the population immunized has a huge impact on the speed at which the third wave recedes.

How huge? Roughly speaking, at current rates, by my calculation below, day-for-day. We’re currently vaccinating about 1M per day. Every 3M persons vaccinated brings the date of the end of the third wave forward by roughly three days.

All bets are off once the new COVID-19 variants become prevalent. But my contention is that we can get the existing variant under control *in short order*, just by maintaining COVID hygiene and maintaining the current rate of vaccinations.

Details follow.

Below, here’s the way things look if we merely continue the early-January trend.

At the current rate of decline, it will be months before the U.S. reaches a level of 10 new cases / 100,000/ day falls below 10. (The figure 10 is arbitrary, but that’s my proxy for “the U.S. pandemic is under control.)

Now let me do a little arithmetic, on-camera. If math isn’t your thing, skip to the boldface conclusion below.

Let me take the equations that I calculated in Part II of this series (Post #979), and tweak them to match the current observations. To my surprise, it doesn’t take much to get that. Recall that in that prior post, I came up with an R-value of 1.1 this way:

- 3.33 * (1 – (.3 + .53 – .3*.53)) =~ 1.1
- 3.33 = R-nought, the original (zero-precautions) viral replication factor.
- .3 = 30% of the population immune via infection (or vaccination).
- .53 = net effect of existing COVID hygiene (masking/distancing/etc.)

If I change .3 to .41 (the approximate fraction of the population currently immune via infection or vaccination), and just slightly tweak the estimated value for the COVID hygiene measures, I can get:

- 3.33 * (1 – (.41 + .54 – .41*.54)) =~
**0.90**

The .90 then matches my estimate of the current US viral replication factor (table shown above, bottom line). And so, the current 10%/cycle decline in cases, on average, for the U.S., appears fairly consistent with the estimated fraction of the U.S. population currently immune.

Great. Now look what happens if I add a month’s worth of vaccinations, or a further 12.5 percent of the (U.S. adult) population.

- 3.33 * (1 – (.535 + .54 – .535*.54)) =~
**0.71**

Why does that matter? Well, abstracting from the time lags involved in immunization (e.g., six weeks from first shot to full development of antibodies), **at that new, lower viral replication rate, it would take just three weeks to bring the U.S. rate down to 10 cases/ 100K/day.**

My point is not the exact set of estimates I’m using. **My point is that if we are, as I assert, near the “remission” herd immunity level already, the effect of vaccinations on the viral replication factor “R” is quite large. **

**Right now, conventional wisdom tells is that we’re in the business of using vaccinations to achieve some far-off goal of herd immunity**. We’ll get immunized as a matter of self-protection, but we’re not expecting to see any material benefit to society until mid-summer or so.

**I think that’s wrong,** due to the misinterpretation of herd immunity that I have been discussing in this series of posts. **In fact, we’re using vaccinations to push well past the point of “remission” herd immuni**ty — the point where the viral replication factor dips below 1.0 due to the combined effect of immune population and COVID hygiene measures. **And that takes what would otherwise be an agonizingly slow decline in the U.S. case rate, and vastly speeds it up**. If we could magically add a months’ worth of vaccinations right now, we would reduce the length of the U.S. COVID third wave three-fold.

**Let me just sum that up in a single estimate of impact. ** At the margin — at the point where we’ve added in a month’s worth of newly-vaccinated individuals — adding another percentage point to the fraction of the population vaccinated (or three days’ worth of vaccinations) reduces the time needed to reach 10 cases/ 100K /day by about 2.5 days. (Again, based on the calculation shown above). At that point, **every day of vaccinations brings the date of the end of the U.S. COVID third wave forward by almost a day.**

Now, that’s an exaggeration. It will take time for those vaccinations to be delivered, and a further six weeks from first shot to full development of antibodies.

But the main point remains the same. People are discussing vaccines as if they’ll have some effect on the pandemic some months from now. Because they’ve gotten this “70%” figure stuck in their heads. But that’s not the right figure. And so that’s not the right conclusion.

The upshot is that not only can you believe in herd immunity and vaccinations, a proper understanding of herd immunity means that you should grasp the strong positive synergy between the two. Right here, right now.

But you will grasp the full potential for synergy only if you can:

- acknowledge that approximately 40% of the population that has already been infected with COVID and so is already likely immune;
- understand that the classic 70% herd immunity number is for the effect of herd immunity
*in isolation (no other precautions taken)*; - understand that you only need about 40% of the population immune to drive the viral replication rate below 1.0 i
*f that is used in conjunction with our other precautions (masking/distancing/limiting)*; (This is what I call the “remission” level of herd immunity); - realize that 1% of the population vaccinated is 1% on top of the (remission) herd immunity level.
- grasp how leveraged that is, via the algebra presented above — that every 1% vaccinated comes out of the (effectively) 30% of the population that is still responsible for spreading COVID;
- grasp how that is further leveraged via compounding of multiple generations of viral replication.

I realize that it’s a lot to ask, to get through all of that. But if I can do it, I assume a lot of other people can too.

**But how will you know if I’m right nor not?**

The gist of what I’m saying is that you should expect the current rates of decline to accelerate noticeably as vaccination adds to the existing pool of immune persons. All other things held equal.

Back-of-the-envelope, in one month’s time, the U.S. average rate of decline in new cases/ 100k/ day should look more like the current Pacific region (essentially, California) rate of decline.

So one way you’ll know if is that comes true. That’s no guarantee that I’m right, but it should shift your subjective estimate of whether I’m right or not.

But a second way you’ll know is of you see this in the newspaper. Surely, some credentialed academic out there can do the same calculations I’ve done, and reach the same conclusion. You just have to shake the cobwebs out of your brain and realize that everybody uses the term “herd immunity”, but nobody is thinking very hard about how it has traditionally been estimated.

I don’t routinely point this out, but I tend to be ahead of the pack. E.g., in March, I shaved my beard so I could wear an N95 to protect against aerosol transmission of COVID-19 (Post #587). At the time, the CDC did not even recommend wearing masks at all, let alone masks capable of dealing with aerosols. So I felt a bit like a nut, wearing an N95 to the grocery store, back then. But I wore it anyway.

That track record doesn’t mean that I’m right about this. All it means is that it doesn’t particularly bother me that no credentialed academic is saying this. Yet. Give it another week or two of decline, and surely somebody with the right credentials will independently figure out the logical and algebra presented in this series of posts. And at that point, you can read it in the papers.