That's absurd. Why do you think that a particular smallpox or measles epidemic dies out? Because enough people have been infected in a given population that it

That's absurd. Why do you think that a particular smallpox or measles epidemic dies out? Because enough people have been infected in a given population that it can no longer spread in that population. That doesn't mean the disease will go extinct, but the epidemic will end in that population. Flare ups can still happen among sub groups of people in the population who aren't immune but the disease won't spread rapidly through the population as a whole until the number of people who are immune drops below the herd immunity threshold for that particular disease/community.