Only thing that works for rats, big rats are poison and traps, like most others.
Buy bait stations, at Tractor Supply, or Coop etc. About 15-17.00. Buy a bucket, of baits, for 20.00. The baits fit over wires, in the big bait station and they can't drag it off. Kids and pets can't get it. It is not Decon or Warfram now.
Buy some Decon pellets and put them where kids won't get them. If they do it is not deadly to kids, usually. It is blood thinner. The rats eat it and die, of thirst, even if they drink.
Not so small live traps, from Co-op or Tractor Supply, for rats, squirrels etc or others and make sure to leave no scent on it and bait it with peanut butter.
Sticky Traps. They make large sticky traps. Caught about 3 lb rat on one. I had one, of the critter, sit on the sill plate and attempt to be friends, not really. Wasn't afraid. The woods are full of these things now.
A good rat terrier or Dacshund(misspelled) or feist. Might take a bit of prompting or training. They are a better bet than most cats. It might be an even bout between a cat and some, of these, rats.
Block off opening or put in new screen with large wire in it. They will chew out small wire. They will eat through, low spots, in mortar joints, in foundation or walls. They can chew through the concrete. treated lumber. One chewed through 2x10 may have been treated.
The foam sealants come in two kinds. One slightly expands. One expands, to fill large holes. Rodents won't eat the stuff. Fill all cracks and low places between block etc and sill plates.
Use home defense, on outside, of foundation, and sill plate and inside every few months. Kills bugs that come in contact with it and rodents don't like it.