They're always a problem around chook pens. You can't ever really get rid of them unless you pick up every grain before going to bed... Let's face it, life is too short.
Poisons are reasonably effective, but not nice to use. Last time (in desperation) I laid out baits, I killed an antichinus and a ringtail possum. It was very distressing, as I hadn't realised such animals also take baits (or perhaps eat poisoned rat carcasses). But the blue stuff in their dying droppings was fairly obvious.
I've been trapping successfully for quite a while now, using the mesh brooder with a little sleeve-insert made of rods that all point inward. I only trap when rat numbers build up, and this seems to keep overall populations fairly low. For instance, the first time I used my brooder as a trap, I caught 21 rats in a single night. The most I've caught since then is 10; usually it's only one or two.
The art is to place the cage near rat burrows and leave the cage doors open for a few nights, with ordinary chicken feed inside. Only when rats are happily coming and going do you shut the doors and force them to use the sleeve-insert as an entry tunnel. Then they can't get out, and next morning they can be caught in smaller traps and dispatched as humanely as possible (one method is just to put some snap-traps in the large cage, or I suppose you might use baits, though you would want to leave drinking water in the cage so as not to be cruel. Death from baiting can take nine days!).
There are plenty of warnings on the net about handling dead rats (Weil's disease spread by broken skin touching rat urine, for one), so I always wear gloves when dispatching them, and scrub like a surgeon afterward. Amazingly, in some countries rats are eaten by people. I'm sure these are country rats, not urban or suburban ones! I'm almost ashamed to add that my dog eats rats after catching them, though she usually leaves the rear end untouched. Sometimes you just have to trust your dog to know what's best...
Meanwhile, to someone who's trying to get back to natural foods for chickens, it seems strange to bury fresh protein by the bucketful while buying layer feeds containing artificial methionine and other amino acids... But everyone has their cut-off point, and rats are mine.