I was curious what the percentage of previously recovered in this chart was.
So I looked it up.
Hypothesis: The previously recovered are a “significant fraction” of both the vaccinated and unvaccinated populations. (TLDR: Depends upon whether you consider 6-10% a “significant fraction.” )
[Mortality rate is typically expressed at deaths per 1,000 population per year, however, the x-axis here covers only ~6 months, and data points appear to be weekly counts, which would make sense, because the CDC publishes data weekly in its Morbidity And Mortality Weekly Report. So at this year’s peak, the mortality rate for “unvaccinated” was about 10 per week, while “fully vaccinated, all vaccines” was just under 2 per week, which is entirely consistent with the latest reports that the vaccines are highly effective at preventing deaths from COVID-19.]
Same source: OurWorldInData.org/coronavirus
Total cumulative COVID-19 cases (US):
52.79 million (as of 12/27/2021)
Total cumulative COVID-19 deaths (US):
816,533 (as of 12/25/2021)
52,790,000 - 816,533 = ~51,973,467 recovered Americans
So what’s that as a percentage of the U.S. population?
U.S. population (census.gov):
331,893,745 (est. as of 12/29/2021, at least when I looked at it, it’s gone up since)
~51,973,467 / 331,893,745 = ~15.66%
% of U.S. population fully vaccinated
61.33% (as of 12/27/2021)
[vs. only ~15.66% who’ve recovered from COVID-19]
331,893,745 * .6133 = ~203,550,433 vaccinated Americans
Conversely...
331,893,745 - 203,550,433 = ~128,343,312 unvaccinated Americans
If the two groups are assorted independently (which is probably not the case), the probability of a given person being both fully vaccinated and recovered is:
.6133 * .1566 = ~9.6%
or roughly 331,893,745 * 0.96 = 31,875,998 people.
And the probability of a given person being both unvaccinated and recovered is:
1 - .6133 * .1566 = ~6%
or roughly 331,893,745 * 0.06 = 19,913,625 people.
So, taken just as a probability, there’s a greater chance of a randomly selected person being both vaccinated and recovered, simply because vastly more Americans have been vaccinated than have contracted COVID-19 (which is what we want).
ADDENDUM: The total number of "cases" is likely higher than 52.79 million, because some people (including myself) recovered from COVID-19 without being a confirmed "case" (I later had a rapid antibody test, but not a confirmatory PCR test when I was sick). OurWorldInData.org notes that "Due to limited testing, the number of confirmed cases is lower than the true number of infections." Thus the percentage of Americans who've recovered from COVID is likely larger than 15.66%. The numbers for vaccinated and unvaccinated, by contrast, are much firmer, since they're better documented. I used only the "fully vaccinated" number because that's what was used in the mortality rate graph. The numbers of deaths from COVID depend upon the attribution of cause of death, which is somewhat subjective ("challenges in the attribution of cause of death" as OurWorldInData.org puts it), so should probably be considered an upper bound on the actual number. The percentages I calculated are probably conservative, but should be pretty good, considering the large percentage of fully vaccinated Americans.