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The comment above is overstated, but more or less correct. All the naive herd immunity calculations assume a well-mixed population. A large fraction of recovered and immune young people will protect the elderly from contacts with their children, with store clerks, etc., but not from contacts with other elderly. If we successfully protect the elderly, then herd immunity among young people will decrease the probability that the virus gets introduced into a nursing home; but it does nothing to slow the virus's spread once it does.

That heterogeneity also goes the good way though, since people in jobs most prone to spreading the virus (doctors, nurses, store clerks, etc.) tend to get infected first and therefore become immune first. There are models suggesting we might reach overall herd immunity with only ~30% infected (https://news.ycombinator.com/item?id=23149725), though this is obviously speculative.




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