Don't forget the rats in Guards! Guards! as well.
And all the rats in Feet of Clay - they play quite an important role.
I think Terry is fascinated by rats and how they've become sort of attached to humanity. There's a saying about how you in a city you are never very far from a rat. And we've got a culture that vilifies rats as being dirty and spreading disease. Even the word 'rat' has become very negative. If you call someone a rat, you usually mean it in a negative way.
And yet, anyone who has ever had a rat as a pet will talk of intelligent, friendly and very clean animals.
I can imagine Terry being interested in this apparent contradiction.
I don't know if he's ever had pet rats, but I do remember that he did a lot of research on them when he was writing Amazing Maurice - I don't have the book to hand, but I think there's an author's note about it in the book.
Terry is a cat person. He has loads of cats living at his home, so I suspect he doesn't come across too many rats - unless they are gifts from his cats.