All rentals come with the "implied warranty of habitability," or the obligation on landlords to provide premises which are fit for their intended purpose--in this case, residence. While  the occasional rodent does not violate that warranty--the law does not require landlords to be perfect and provide completely rodent-free living--a significant rodent problem may breach the warranty. If the warranty is violated, then the tenants may be able to do one or more of the following: pay for exterimination themselves, then deduct the cost from their rent (called "withhold and deduct"); sue the landlord for compensation (a pro rata rent credit for the time they lived with rodents); seek a court order forcing the landlord to deal with the situation; or for very serious cases, treat the lease as terminated due to the "constructive" (or effective) eviction of having a major habitability issue. It would be best to consult with a landlord-tenant attorney to see if this case is serious enough as to violate the warranty and, if so, to determine the best course of action.