The exact percentage required depends on the R0 of the disease, the number of people each contagious person can be expected to spread the disease to assuming no

The exact percentage required depends on the R0 of the disease, the number of people each contagious person can be expected to spread the disease to assuming no prior immunity. I think you can think of it this way: if each person would otherwise spread the disease to two other people, but half of the population is immune, they're only going to be able to pass it on to one other person. In reality it's probably more complicated than that though.