Per code 83.51, rodent control is the landlord's responsibility:
(2)(a) Unless otherwise agreed in writing, in addition to the requirements of subsection (1), the landlord of a dwelling unit other than a single-family home or duplex shall, at all times during the tenancy, make reasonable provisions for:
1. The extermination of rats, mice, roaches, ants, wood-destroying organisms, and bedbugs. When vacation of the premises is required for such extermination, the landlord is not liable for damages but shall abate the rent. The tenant must temporarily vacate the premises for a period of time not to exceed 4 days, on 7 days’ written notice, if necessary, for extermination pursuant to this subparagraph.
There is a disclaimer stating that landlord is not responsible if the condition is created by the tenant:
(4) The landlord is not responsible to the tenant under this section for conditions created or caused by the negligent or wrongful act or omission of the tenant, a member of the tenant’s family, or other person on the premises with the tenant’s consent.
If the landlord fails to remedy the situation it can be considered constructive eviction and the tenant can terminate the lease. It is considered a violation of the quiet use and enjoyment covenant inherent in all properties.
It is best to hire an attorney to ensure the landlord is in violation of the statute otherwise the tenant would be liable under the terms of the lease.