Here are the four important characteristics of these kinds of diseases:
- They spread rapidly and efficiently from person to person. This means that everyone in a given area gets the disease all at once.
- They are "acute" illnesses where you only have them for a short time. You either die quickly or recover. This means that a lot of the people who could get the disease die. Then the disease has fewer people to infect.
- The rest of the people (the ones who don't die) become immune. This means the disease can't spring up again in the same population.
- The diseases have to have human hosts -- they can't live in the soil, for example.
So all of this means that the disease sweeps through and kills a bunch of people but then it can't stay there any longer because there are no potential hosts. It goes away and can't return until there's a new generation living in the place.