Just to add a tad, the number needed for herd immunity differs by disease. For polio, you only need to get around 80 - 85% of the population immune before everyone is effectively protected. For measles, on the other hand, you have to get to 95%. That's one of the reasons polio is expected to be eradicated before measles, every % point higher is harder to get, so 95 is a tough goal to reach.