Yeah, I'm not an epidemiologist but I think the principle is simple: it's just a matter of getting the actual transmission rate below 1, so that any outbreak will naturally die out. If in the absence of any immunity the average infected person infects 3 others, but now 2/3 of people are immune, then the average infected person will actually only infect one other. Ditto for a transmission rate of four and 3/4 immunity, and so on.
It's worth noting, though, that the natural tendency during an epidemic is for the total number of infections to exceed the herd immunity threshold; I think the phrase to google is 'herd immunity overshoot'.
(It's also worth noting the serious problems with this study, as pointed out by other commenters.)
I saw that too when mucking with simple models. The percent infected overshoots (R0 - 1)/R0. So that is a threshold for herd immunity not the ultimate infection ratio. They're only equivalent under steady state conditions.
Also saw an study released by the CDC that estimated that the initial r0 in Wuhan was 5.8. Explains what happened in Northern Italy and New York. The epidemic achieved break out while most infected were still mildly ill or asymptomatic.
It's worth noting, though, that the natural tendency during an epidemic is for the total number of infections to exceed the herd immunity threshold; I think the phrase to google is 'herd immunity overshoot'.
(It's also worth noting the serious problems with this study, as pointed out by other commenters.)