Damn. I live somewhere that doesn't have rats, because if there were any around the hawks, owls, fox, raccoons, bobcats, coyotes and black snakes would eat them.
I had a property once in the city that had a rat problem around it because of sloppy-*** neighbors and the only thing that could be done about it in the end was get an exterminator. You need to be killing off the rats at high speed, and you usually can't do that with just a trap unless you have dozens of these traps around, so poison bait is generally your best bet. Especially in the case of rat litters, where the mother will bring the poison back to the nest.