They[rodents] are VERY opportunistic.
I lived in a cheap apartment complex when I was 19 yrs. old. They were infested with roaches. I had the only roach free apartment, in very short time. You have to be very aggressive with vermin.
Seal all approaches into your house. Monitor constantly. Poison and trap as it becomes necessary. I would say the landlords won't deal with it because it is an all too simple process. Some people are just not stringent enough to avoid problems. The landlords don't want to spend hundreds, when $20. and a little bit of gumption will get rid of the problem....