Here in Michigan, there are over 60,000 deer/auto accidents every year with most of them occurring here in S.E. Michigan where deer inhabit small forested areas among subdivisions where hunting is prohibited.
In fact, if you would like some fresh venison, there is a dead deer that was hit by a car at the entrance of my sub yesterday. Come and get it......
But I digress, what is your point? What is your solution to the rat infestation in New York? Trap and sterilize and release?
No rats are rodents and are problematic for humans.
Cats and Dogs were domesticated by humans thousand of years ago and are no threats to humans.