Traps aren't going to solve the problem. The problem is that the feed is attracting the rats and mice and soon the predators that prey on them like hawks, owls, snakes, and furry predators. Shut off access to the feed and you have won 99% of the battle as there is little for large populations of rats and mice to live on in most areas. There will be natural foods but you are forcing them to forage constantly instead of coming to the buffet every night and day. Plus the foraging puts them at risk to predators that naturally keep their numbers down. And when there is plentiful food, rats and mice breed faster with larger litters.
You need to first secure all feed in a metal trash can, second get a good treadle feeder, inward swinging door, spring loaded door, and with a big counterweight to stop the mice from just pushing the door open. Just google rat proof chicken feeder or treadle feeder and read the reviews carefully especially the negative reviews. Nearly any feeder will work at first when the mice and rat population is low but so many of the pretty feeders can be pushed open by the smaller rats and larger mice. Do a search on the Feeding and Watering your Flock forum too.
This is an old problem that has been completely solved years ago if you spend the $100 it takes to buy a large feeder and get it shipped to you. A plus is that shutting off access to the feed makes poison ten times more likely to be eaten. But you don't need to poison, wait a week and the rats and mice will be gone.
