Chicken keeper here, if you have chickens, rats will try and move in. If your neighbour will cooperate get them to minimise the amount of food available - treadle feeders are good, but take a bit of training for the chickens
Locate the runs they the rats are using and place bait boxes across them, make sure you wear gloves when handling to avoid making them smell of humans. I've found the grain bait much more attractive to the rats than blocks, but of course make sure non-target species can't get access. Keep bait topped up for at least a week after they stop taking it. Rats are naturally cautious so it may take some time for them to trust a new food source or strange new objects in their run.
If you can find someone with a good ratting dog, they will have the time of their life