How can you avoid mice in your hospital?
There is a lot of wild speculation about this on the internet.
From my experience, I believe the mice always appear regardless of what you do, but they have no effect on anything (patients don't complain, health inspectors doesn't care etc.).
The only thing you can do it kill them with your cursor, which creates mess that has to be cleaned up and you can get an end-of-year trophy if you kill lots of them.
Some people claim that mice create epidemics, others that you can keep their levels low by keeping your hospital warm and/or placing items (like drinks machines) in front of their holes. I don't think that's true...
I don't think you can.
However, to add to vesan's information, you can also get rid of mouse holes by putting a bench in front of the hole and then removing it.