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Rats

Rats/Mice are attracted to Food, and Secure Warm Places to Hide.
Remove those, place and maintain preventative traps (for the determined hold-outs) and you won't have a problem.

To Kill Mice/Rats:

Even with an overlooked, hidden nest, vermin need to eat VERY often, and without food will move on VERY quickly.

Hiring an exterminator is often useless until you do the following tasks. Sometimes just a reminder is all is required:

No matter the number of pests, diligently trapping, and removing critters will quickly solve your problem. Often in one or two weeks. Keeping a casual eye in the future will prevent them coming back. Keep on top of it!

Traps:

Must Watch Mousetrap Mondays
400 Year old Mousetrap
Walk the plank