[Acne] Sulphur+salicylic acid for staph infection on the back?

UPDATE: 24 days into the routine and things have improved a lot!!

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My friend has had very nasty bacne for more than a decade, which the dermatologist has diagnosed as Staphylococcus aureus. He's taken 2 rounds of antibiotics in the last 2 years, plus some other topical creams prescribed by the doctor, but it didn't go away.

Now, since we're self-isolating together, I've applied a sulphur + salicylic acid shampoo (for dandruff) on his back almost every night (I thought it couldn't hurt to see what happens). We're one week into this routine and most active pimples have dried out and the scars have faded (I'm guessing because of the exfoliation).

Has anyone had any success using these ingredients in the long run? My friends says that the staph always comes back, regardless of the temporary improvement he may see when using one treatment or the other. I couldn't find any compelling information online about their efficacy.

Also, any other effective treatments anyone knows of (besides the antibiotics, which seem not to work) to permanently heal this?

Thanks!!