We had two phase outbreaks with the Spanish flu, maybe more smaller ones. Finally it went away so somehow it stopped spreading.
Watch countries that don't get it, if any, and look how they kept it out, if they do.
The bubonic plague has an antibiotic now, but the side effects are awful, we also know how to control the fleas which carry it, and it is tough to spread in decent sanitation levels. But bubonic plague is at the same class as a disease as Ebola is: class 4. Plague is still dangerous even with the antibiotic.