It could be chinch bugs or a fungal disease. To be sure and before you purchase any particular spray I suggest you take a sample to your County Extension Office and see if they can identify the problem and if necessary prescribe an appropriate remedy. Take a 4" X 4" sample of sick not dead turf and place it in a ziplock bag so nothing escapes.
Their contact info is:
Collier County UF/IFAS Extension Office
14700 Immokalee Road
Naples, FL 34120
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