First, these diseases are very effective at spreading from person to person. Many of them spread through mucus and water droplets, which are created by coughing and sneezing, symptoms that the germs themselves create. This means most people in the population are exposed to the disease in a very short amount of time. Second, they are also very "acute," meaning that when they kill, they usually do so with relative speed. Those people who do not die recover almost as quickly, which leads to the third characteristic, the fact that these diseases leave those they don't kill immune to further outbreaks. The last characteristic is that these diseases need human bodies to survive. They can't live long separated from humans, either in water, soil. All of these factors predispose these diseases to a certain pattern. They strike quickly, affecting a large swath of the population. Those affected either die or get better, and, either way, they can't get the disease again. So the germs that cause these epidemics quickly run out of victims. They can't come back again until enough people without immunity to them have appeared in the community, either by birth or large-scale immigration.
Source: Diamond, Guns, Germs, and Steel, 202-203.