Where the threshold formula comes from
Herd immunity is the indirect protection of susceptible people that emerges when enough of a population is immune to keep sustained transmission from taking off. The classic threshold is 1 minus 1 over R0, where R0 is the basic reproduction number. The more transmissible a pathogen, the higher its R0 and the larger the immune fraction needed.
This is why highly contagious measles, with a very high R0, requires roughly 95 percent immunity, whereas seasonal influenza sits much lower, around 50 percent in simple estimates.
Why the simple threshold is only an approximation
The basic formula assumes a uniformly mixing population and lasting immunity. Real populations mix unevenly, immunity from infection or vaccination can wane, and new variants can change transmissibility, all of which shift the practical threshold. Estimates for SARS-CoV-2 omicron in the region of 85 percent reflect those moving parts and carry real uncertainty.
This is general educational information, not medical advice. Vaccination decisions and population targets are set by qualified public health authorities.