Post #993: A couple of bits of confirming evidence on herd immunity

Posted on February 4, 2021

This article on herd immunity in India was published in today’s Washington Post.   I thought I’d bring it to your attention.  Not just for the content regarding herd immunity as the likely explanation of the current state of COVID in India.  But also for an official estimate of total U.S. infections that seems just slightly lower than the one I  have been using.

Currently, India seems to be doing fine, with low rates of new COVID infections, and little in the way of restrictions.

The explanation per Indian epidemiologists is that new case rates are down because such a large portion of the population has already been infected.  That’s based on the presence of antibodies to COVID in a sample of blood draws.   In some large cities, more than half the people have antibodies for COVID-19. 

And, probably more interesting from a science-y point of view, in the cross-section, regions with higher prevalence of COVID-19 antibodies (higher historical infection rate) have the lowest rates of new cases, per this scholarly piece.  (There’s not a lot of statistical power there, as I read it, but it was still interesting to see that result.)

They seem to cite something in the low-50-percents for achieving control of the pandemic via herd immunity.  That’s combined with (e.g.) continuing to use masks and such in at least some public situations.  (So, not 50% for herd immunity in isolation, but 50% when combined with some other COVID hygiene.)  But India also appears to have had a much milder set of cases, on average, than other countries, or has some sort of genetic-based immunity.  The reported death rate from COVID are a small fraction of those of other countries.

But to me, the most interesting tidbit is that some researchers took the CDC US seroprevalence (blood antibody) surveys — with all of their limitations — and ginned up an estimate of total U.S. infections as of “mid-November 2020”.  This is referenced in the Post article above.  The scholarly work is here.  I have not bothered to read the details, because my guess is that any estimate from the CDC’s seroprevalence surveys involves a lot of “structural error”.  Based on looking at the data from those surveys in earlier posts.

I’m just going to take their estimate of ~47M total US COVID-19 cases as of 11/15/2020, and see how that compares to what I’ve been using.

Bingo.  Their results almost identical to what I got, when I looked at the CDC seroprevalence data a while back.  I found 5-to-1 for older seroprevalence data, and 4-to1 for newer.   They found that the ratio of total cases to diagnosed cases, for the entire period up to November 15, 2020, was 4.22.  (I calculated that, by comparing their 46.9M 11/15/2020 total to the NY Times COVID Github repository figure of 11.1M diagnosed cases through 11/15/2020.)

Extrapolating using that 4.22 ratio, the current diagnosed count of 26.6M COVID cases implies an actual total of 112M persons who have been infected with COVID in the U.S. currently.   That of course assumes that the ratio of total to diagnosed cases hasn’t changed since mid-November 2020.

(If anything, that’s probably a conservative estimate, due to the persons who apparently simply did not bother to get diagnosed over the holidays.  See Post #929 for the “dips” diagnosed cases over the holidays.)

That’s only modestly lower than the totals I have been assuming.  I’ve been using 5.0 as my ratio, for a number of fairly vague reasons, outlined in


If I were to substitute that 4.22 multiplier for the 5.0 multiplier I have been using, you’d get the following comparison as of 2/3/2021.

That would lower my estimate of the fraction of the population currently with immunity by about five percentage points.  Here’s my estimate using my 5-to-1 multiplier, and then this alternative 4.22-to-1 multiplier.

I don’t think that changes any of my other calculations in any significant way.