In the history of mankind, we have managed to eradicate a grand total of one human virus, smallpox, and it took about 150 years of vaccinations to do it. We almost managed to eradicate polio after only 75 years of vaccinations, but cases kept popping up in the wild in Afghanistan, Pakistan and parts of Africa.
Thanks to Brandon, we now have millions of migrants streaming into the U.S. from all over the world.
If there is an as yet unidentified animal host, then it polio will never be eradicated. Smallpox was a human only virus which is why we could eradicate it.