They're common, here.
We leave them alone.
Them and deer are the most common roadkills, unfortunately.
Interesting that ticks are a food source.
I agree that they do look like rats. A decade ago we had a German exchange student that stayed with us. The cats drug into the house (through the pet door) a possum and she was the first to see it. She came running to me and in a heavily stilted German accent told me, “BILL, THERE IS A RAT IN THE HOUSE! A VERY VERY LARGE RAT!” She stood by and watched me throw a towel over the “rat” and take it outside and place it over the fence. After explaining what it was and her watching how I calmly handled it, she told me, “Well, it may be a possum, and it may not be a rat, but it will always look like a monster rat to me.”