Have passive and active defenses. A passive defence is a sticky trap, or a classical mouse trap along routes they are expected to travel, such as door arches, around garbage, inside of food pantry shelves. A active defence is rat poison, a cat, locating and sealing off rat holes.
Assume they have Interior Lines where they can absolutely exclude you physically from seeing them or interfere with then directly within a wall. The world of their exterior lines are your interior lines. They can go anywhere you can. You need to start making strongholds they can't easily breech, like plastic containers that lock down with hard snaps instead of plastic bags. This was a innovation of the Cycladic Culture of Bronze Age Greece, they figured out putting big heavy lids on their household grain bowls kept critters out.
Reducing their preferred targets for food, you can control and bait them into places that remain and put the poison there. You place the passive traps along the way.
That's the nature of Poliorcetica. Siege warfare, but against rats. You can't keep them out, but you can deny them what they want and lead them to where they cannot possibly survive. It's a war of attrition, a battle to the death.
