Where I live was heavily infested with rats when I moved here. The owner lived here until he was put in a nursing home and had left a stockpile of grain and bird feed. The out buildings,porch of the house were loaded as they had 2 years without human interferance.
I took away all the grain, bird feed , etc. and put a lot of poison out and kept it out until the rats were gone. I think about 1 month took care of the problem. I got a cat to do the rest and seldom encounter rats any more but once in a while I,ll spot some activity. Always try to eliminate as much as you can their food source and make it easy for them to get at the poison while protecting your other animals from eating it. I have had cats get to rat poison and witnessed them vomit it out but am not aware of it killing them. I understand rats and mice don't vomit so it kills them. Don't go after them half heartedly, but be aggressive and be careful not to kill anything you don't want to. Same with moth balls. Use plenty and keep them up and they will repel most animals most of the time.