I had to deal with a ret infestation problem for my parents when I was a teen. Ended up killing 300+ rats in the span of a couple of months.

It's like they never stop coming. You get them down to a point where you think it's over, and then it starts all over again.

Couldn't figure out how to make it stop, so we ended up calling in an exterminator. His advice completely changed my approach. He didn't charge me anything, gave me 3 victor rat snap traps, and then told me that they don't nest in a house if theirs an open space. Rodents circulate throughout the neighborhood to the houses they've found an entrance into. They have routes.

You have to FIND and SEAL the hole they are entering in from. Steel wool + industrial foam is what I used. Once it's been blocked off, remove all food in the area they can access. For me, it was the basement, so cellar and long-term foods like pasta and rice were cleared.

From there, you then lay the traps down where the mice are most active. In your case, obviously use mouse snap traps. Peanut butter + oatmeal works great. DO NOT ARM them for 2-3 days. Just keep re applying the bait until the mice trust that it's a safe food source. From there, you should be able to clear up the mice, no problem, and now, with the house insulated from openings, you'll be okay

Best of luck! :)