

This study, in a "pier reviewed" journal, meaning that you should drink a beer on a pier while reading it, thinks that 20% to 30% is
needed.
You can get the PDF here, it is an OK read if you are in the medical or engineering profession. They state their methods and assumptions clearly so you can follow, it is not JUST a mathematical proof.
https://arxiv.org/pdf/2008.08142.pdf
It is interesting that they used the Descriptors R(0) and R(OE) which are coincidentally the exact ones that I modeled with. R(O) being the initial multiplication number (reproductive number) and R(OE) being the "Effective Reproduction Number" which changes over time
https://www.westernjournal.com/new-study-argues-covid-herd-immunity-may-already-reached-regions-us/
“Taking the effects of biological and social heterogeneity on COVID-19 transmissibility, the researchers calculate that the herd immunity threshold is likely somewhere between 20 and 30 percent of the population,” Bailey wrote
This more is more a description of"where we are" in the Lock Step cycle, I covered heavily before, read and reported on all the back ground material.
https://www.activistpost.com/2020/08/the-rise-of-authoritarianism-from-parasite-stress-theory-to-lock-step.html
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