I am infested this winter. I didn't catch it until we were about 2-3 generations in. It's BAD.
In two nights, with two traps, I have hauled out 44 rats. (It would have been 60+, except one of the doors malfunctioned and got stuck open after a massive chonker jumped on it going inbound. Everyone left.) I think the door malfunctioned because the trap was set on a slightly angled bit of the coop floor, with a slight angle the wrong way making the door not want to close as much as the weight was able to pull. So when you set these, they need to be perfectly level or with the door part angled slightly downward so it's more inclined to reset. Or maybe wrap the weight bar with wire if your situation doesn't let you control angle - it wouldn't need much to make it a bit more heavy.
Tractor Supply had these on sale last week about 30% cheaper than I could find them anywhere else.
These are, by far, the BEST rat traps I have ever owned in my life. To dispose of your myriad of rats, you just toss 'em in some deep enough surface water (I use a creek) or they come with a perfectly sized drowning tray to fully submerge the rat trap. (The manufacturer calls it a "safe transport tray" in the packaging, but I think they mean transport to the rat afterlife.) Then do whatever you like with the carcasses. Feed the crows, the chickens, the worms, or the dump rats. Whatever - they're perfectly non toxic.
Best bait so far: Potato flakes, peanut butter powder mixed in, leftover Xmas cookies/candy, and dried grub worms. Also, last night, I found half a rat when nothing other than the other rats in the cage could have got it, so possibly dead rat is good bait too.
Edit: I should note, this is not an easy task for me. I used to keep pet rats. They are actually very friendly adorable creatures if you tame them down from childhood. But I can't have this much disease vector in my coop.
Edit 2: The design of these things is freakin' genius in it's simplicity. It reminds me of primitive fish traps.
Edit 3: Cottonseed meal (commonly sold as a relatively inexpensive fertilizer - 40 lbs for 60 bucks shipped(ish)) is an effective birth control agent in all mammals. The chemical with the magic function is called gossypol, be sure you read about it before following the next bit of advice. Make rat cookies and keep the cookies always available in bait stations where nothing can get it but the mice and rats. Effectiveness wears off about 4-6 weeks after stopping the feed. If you breed other mammals that eat rats/mice intentionally, this could harm their fertility as well. Throw a cat in the coop at night, bait stations with rat cookies, and leave the traps set. This is my current plan. And then shoot whatever's left with a revolver and rat shot if needed.