I can speak to this from firsthand experience, as the former owners of my house had an infestation of mice AND rats behind all the finished basement walls and ceilings. It was so extensive that entire basement had to be gutted at the cost of thousands of dollars by guys wearing hazmat suits and spraying disinfectant on everything afterward. That's what can happen if you don't get rid of rodents.
Rodent infestations are not to be taken lightly. As the OP mentions, they can carry hantavirus in their droppings, fleas in their fur, and will chew anything up to and including electric wiring insulation and PEX piping. They bring in food (acorns, seeds, anything they come across) and cache it, which in turn attracts insects.
If you have one or two mice, traps will take care of them IF you also make sure that EVERY possible way for them to get into your home has been blocked. Mice will get through a 1/4" opening but they will chew a smaller one in order to make it big enough. Rats need 1/2" but again will chew a smaller opening to make it bigger. Both will chew right through useless stuff like silicone caulk and spray insulation. A combination of copper or steel mesh plus concrete patch is what you need. Or a decent gauge piece of metal.
Most ultrasonics don't work. Peppermint oil etc doesn't work either, despite the "old fashioned" hype etc. because they will simply avoid the spot where the peppermint is.
Cats do work but no help if the homeowner is allergic and can't own one, or doesn't like/want a cat. Also it's no help if the cat doesn't catch the mice, OR if the entry point isn't eliminated. It all comes back to that one thing:
You have to prevent the rodents from coming in.
Rodents are attracted to places that are sheltered, dark, and too small for predators such as cats and foxes to get in. That is why the interior of finished walls and ceilings, and unfinished attics with fiberglass batts (perfect nesting material, for them it's like the world's biggest and best mouse condo) are what they will head for. The don't like to be out in the open (visible to possible predators) which is why they typically run alongside walls when in a room space.
To the OP: call an exterminator and have them examine your house to find out where the mice are getting in. They will set snap traps and come back several times over the next several weeks to remove the dead ones and re-set the traps, until a week or two goes by with no catches. It's worth the cost. I don't know where you're located but we have used this company in the past for squirrels and mice. Friends of ours have used them for a raccoon issue. It's not a chain/franchise, it's a local company.
https://www.catchacritterinc.com