i've had mice in 2 flats, and an old girlfriend had a full on infestation.
the thing with traps is "for every mouse you see theres five you don't" or whatever the number is. you may kill a few, but you may not solve the problem.
i've had good fortune (so far) with those ultrasonic pest deterrents. you plug them in and the mice bugger off in a couple of days.
maybe they could solve your rat problem?