What do you mean the black plague reached its limit and then died out? What limit? Viruses do not have a time limit on their viability. They will continue to spread and infect forever, if they can find hosts, and don't kill their hosts before they can be spread. This is why the ebola virus actually isn't a huge threat. It kills too quickly. AIDS is more effective, because it incubation period is very long, and shows no symptoms for a long time.
Virus' are not considered life, but they are self-replicating in the right conditions (a host), and as such, are able to mutate. I am demonstrating that which you asked about, mutation and natural selection. The mutation of a virus is what allows virus to be passed from animal to humans, which is where plagues nearly always come from- animals.
I could easily talk of a bacterial plagues, as opposed to virues, which are living things, and which mutated to be able to inhabit humans, from having inhabited animals. It is our proximity to animals in slaughterhouses and farms that have caused almost every plague known throughout history. These virus' or bacterial infections must mutate to be able to infect humans. This is an increase an fitness, by the way.
I have a very hard time believing you were a molecular biologist with statements like the one quoted above, unless I simply misinterpreted what you were actually trying to say.