Am I responsible for Pest Control, or is my Landlord? (Florida rental)?

[rickie]

I am renting a house in Florida, and the detached garage is infested with rats. I have already laid down traps and bait and managed to kill two, but I am still unable to get rid of them. They have destroyed a lot of my property, as well. In my lease, it states that I am responsible for pest control, but the "Florida's Landlord/Tenant Law Summary of Chapter 83, Part II - Florida Statutes" states that "the landlord shall, at all times of the tenancy, make reasonable provisions for extermination of rats, mice, ants and wood destroying organisms and bed bugs." Can I get the landlord to legally do anything to get rid of these rats?