I mean, we have at times considered rats to be part of a literal plague, or in certain contexts where there are vast numbers of them, they've been called a plag

I mean, we have at times considered rats to be part of a literal plague, or in certain contexts where there are vast numbers of them, they've been called a plague metaphorically. But rats in general are not a plague in the context of the whole world, so for a number of reasons this doesn't follow.