An infectious disease needs hosts in order to survive. Generally, the way this works is that the infection enters the host and begins to multiply. That host can then transmit the disease to others, giving the infection further opportunities to multiply. This is a delicate balance because if the host is killed off too quickly, the infection is deprived of the opportunity to spread, and also, if the disease manifests too quickly, people will take precautions to not spread disease, at least theoretically. An infection that seems "successful" to us, meaning that it kills off many hosts and kills them off quickly, is not really very successful because it cannot spread as well. So, given the biological imperative of any living organism, even a plague, once many people are infected, there is nowhere for the organism to spread, and often, the plague has no choice but to slow down, since it has nowhere to go. Another aspect of this is that some people in a given community may develop an immunity or have a pre-existing immunity. Thus, a disease is left with poor hosts. Infections need living people who have no immunity. It may smolder for a while, but generally, the rate of infection does diminish.