First look at the terms of your lease agreement to see who is designated to deal with pests. if it is unclear, then check out whether the pests may breach the covenant of quiet enjoyment, or if the lease has some generic "Landlord breach" section. If the lease doesn't provide you answers, or if the Lease says the Tenant must be responsible, then research online whether your city or state has any protections for Tenants that may put the responsibility on the Landlord. Also check the law and your lease to see if there are other ways for you to break your lease without penalty - which can be used to leave without penalty or as leverage against the Landlord.
[Disclaimer- This information is provided as general information only and should not be construed as specific legal advice as this website is not intended to provide anyone with specific legal advice. No attorney-client relationship is created with the furnishing of this information. This answer should not be used as a substitute for fully discussing the factual nuances of your case with a licensed professional attorney in the state where you are located.]
The remedies available between a landlord and a tenant in SC are dependent upon many variables. First, any landlord who operates more than 4 rental units is subject to the S.C. Residential Landlord Tenant Act (SCRLTA). This is a statute which defines the duties and responsibilites of both the landlord and tenant and describes what constitutes a breach of the duty along with what remedies may be had for the breach. The SCRLTA is codified in Sections 27-40-10 through 27-40-940 of the S.C. Code of Laws. Particularly, Sections 27-40-610 through 27-40-660 spell out the remedies available to a tenant for a breach by the landlord.
Landlord-Tenant rights are greatly controlled by contract law, as well. Where the Landlord and Tenant have entered into a lease, the contractual language of the lease is the determining factor regarding rights and remedies of each party. If the Landlord is subject to the RLTA, the lease may not be made so restrictive as to sign away the remedies available to a tenant under the law.
Your specific rights can only be explained by knowing whether the SCRLTA or a lease or both are applicable to you. Then, a thorough review of the lease would be necessary before an informed response could be given.
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