About 5 years after moving into our current house we had an invasion Norway (brown) rats. These are the wild cousins for "fancy "rats that are kept as pets and are huge. The ones in our house were about a foot long head to rear hunches and about 20 inches head to tip of tail.
The only way we got rid of them was by using kill traps. They pretty much just laughed and ate the bait out of anything else.
Basically we resulted to what @
thomasmryan mentioned, the snap type traps that will break your hand if you accidentally set it off. Even with that, we often would find the traps missing, and later find, by smell, where they had drug it off to die.
We also had to find where they were getting in.
There were two places. I gap of about a half inch between the foundation and cantilevered portion of the kitchen floor, and an area of our porch where the builder failed to cap between a brick wall and the internal wall.
We also had to dispose of a couple of nests in a suspended ceiling in our basement that had babies in it.