Here is a small study on the use of probiotics to eradicate persistent nasal carriage of MRSA (sorry, no abstract available).
Seven patients were instructed to use a lactobacillus nasal spray and a lactobacillus oral suspension (swish and swallow) for 14 days. Five of the seven participants were MRSA decolonized lasting for up to 37 months after treatment.
This is by no means definitive and 14 days of nasal sprays and throat gargles is a bit impractical so the utility may be limited. Regardless, these findings suggests that competition between bacterial species in the nasal ecology can lead to an eradication of nasopharyngeal MRSA.
This is worth further investigation.
