From a Fox News medical consultant:
Currently there have been 17,974,303 Covid cases in the USA out of a 331 million population. That is 5.430% of the population. We are actually gaining 183,927 cases per day. So at this point we are likely getting more cases per day than vaccinations per day. I am not subtracting deaths from any of these numbers since that would not have significant impact.
But in any case we can say for sure that we have at least 5.430% of the US pop with natural immunity post their illness [Not sure for how long after]. Then there is the asymptotic cases. I am sure there are papers that more directly address the estimate of asymptomatic carriers, but using the Stanford paper on the Diamond Princess:
It would seem from my cursory review that you have approximately as many asymptomatic as symptomatic. (I know there are larger multiples reportedly claimed, but just using the study I have on hand to determine the number of asymptomatic vs symptomatic] [Diamond Princess does not match the whole US demographics in age, and other characteristics so it is not a perfect model].
Therefore we would have 10.860% of the population with herd immunity as of today, not counting the vaccinated. The Dr. Makary came to a 25% to 50% of population having natural immunity, not sure how he came to that number (I assume a much higher estimated asymptomatic pop). I do not have high confidence that with 20% of pop vaccinated we will have herd immunity.