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Some states require LLs to exterminate mice, rats, roaches, bedbugs, ants, and termites at the LLs expense. If there is a bomb that must be used to exterminate, you may have to leave your apt for a few days. During this time the LL has to mitigate rent, but does not have to find and pay for a place for you.
Also, do not stop paying rent. If you do, you may be evicted and failure to pay rent is not an excuse even if there is a pest problem (unless the place is literally impossible to live, in extreme circumstances). Failure to pay is basically an automatic win for a LL.
My advice is to contact your LL and let him know about the problem; give reasonable time to cure the problem (probably a week); and if he doesn't cure the pest problem, contact the Clerk of Courts and put your rent money in escrow through the court and let your LL know thats where the $ is.
Good luck