I'm not an expert, and I'm sure it's more complex than this in practice, but if each infected individual transmits the infection to n others, and you assume that a fraction f of the population are immune, you want
(1-f)*n < 1
to avoid exponential growth, so
f = 1 - 1/n
Your examples cover a range of 1.7 to 3.3 as estimates for n, which is roughly aligned with what I've heard reported.