That's “non-zero”; not the same thing as abundant. How do you even know R>1? I'd say “found in wild animals” is the standard for “abundant animal reservoirs”; that's “some animals can catch it from humans” which we already know.
> Smallpox had no known animal or reservoirs.
Smallpox had cases in practically undocumented people. The last few smallpox infections were stamped out by pre-emptive vaccinations of everyone found in the vicinity; that doesn't require the subjects to be human in principle, even if they were in this case.
I maintain we could do it.
> Oh, and BTW, even if we did eradicate it, which we can't, it would still exist in the bioweapon labs of every major country in the world.
Fully-general argument for never bothering to eradicate any disease! Congratulations; I literally cannot rebut this point. All disease eradication is pointless. (By the way, Earth's only got another ~2 billion years of habitability left. Let's just roll over and die now.)