I understand that. But unless each infected mink infects (on average) more than one healthy mink, mink populations are not reservoirs. (You don't need much animal-to-human transmission for it to count as a reservoir, so that's an almost irrelevant point and I don't know why you're focusing on it.)

> Good luck chasing down the smaller rodents. Better not miss a single spot!

They didn't eradicate smallpox by vaccinating every human. I'd encourage you to look it up… maybe start at that Wikipedia page you linked me?