When smallpox was eradicated in the 1950s, it was achieved with something like 100 million doses of the vaccine, which was substantially less than the world population at the time (in the neighborhood of 2.5 billion). This is because scientists understood that the vaccine was not something for individual protection but was rather a weapon to protect the population as a whole (and annihilate the disease entirely) when coupled with a full understanding of how the disease spread.