Don't these things become endemic over time? I can't say I haven't done a lot of reading on Mexico, but the plague lasted for about 300 years in England, reappearing periodically.
It's easy to see how they do become endemic. And despite that, still no immunity by those who are "local" to the worst of these bugs.
My perspective as to bacteria and viruses in general is that they're all here with us all the time, in that we're all present on the planet simulataneously. It's just a case of when what infects the species and once that occurs, others become infected, also. Containment is nearly impossible with larger populations and certainly with mobile ones.
Like the Black Plague...the "mobility" in place by the trade routes allowed the bug to proliferate among humans outside isolated areas in Asia. And look what happened.