I got rats under my outbuilding where my outside dogs go in at night. The rats were attracted by the dog food and were taking over. I hated to have to kill them, but couldn't have so many. I have cats out there, but literally walked in there one evening to find 2 rats eating out of the cat bowl, and the cats sitting over to the side looking at the rats like 'take all you want, don't mind us...'. Those rats were too much for my cats to want to mess with! Mice don't bother me too much, but the rats can get pretty big on kennel rations... come to think of it, once the rats showed up, I didn't ever see mice. Once the rats were gone, the mice came back.
Anyway, at first I used the old-timey snap traps - sometimes would catch 2 at a time in one trap. Use peanut butter. If you only have a SMALL popluation (ie, just found them) then traps may work OK for you if you can find a way to keep the other animals out of them.
I was catching 5-10 rats a week for over a year before I finally gave up and decided to use poison. I was able to put the poison in the building where the dogs couldn't get to it. I put new 'bait' out every day until it got to the point where there was no more bait eaten. Sure enough about 2 days later, it started to smell so bad in the building I couldn't hardly stand to go out to take care of the dogs. They had all crawled up under the building, no doubt, in their holes to die. For over 2 years I haven't had any signs of rats. AND, my dog food bill dropped at least 1/3. They were easily eating the amount of food of a large dog every day.
I actually saw a new tunnel just this week out there - time to bring out the poison again. I'm going to shove the bait block way under there and put a cinder block over the opening so the dogs can't get to it and hope I can nip them in the bud. I don't like to use the poison, but rather poison a couple of rats now than 100s later... At least I know my dogs are so old they won't be able to do much to dig out the poison.
Good luck with the rats - they will pretty much chew through anything and breed VERY quickly. Try to nip it now if you can!
Susan