Marina I find bleach to be the best and most effective. I’ve used it to clean mold/mildew out of apartment bathrooms. These cleaners work well too: *TSP *Tilex Mildew *The Works But, most “mildew” cleaners contain chlorine bleach, so it’s really the best/cheapest/easiest option in your arsenal. BTW-Have you tried to remove the caulk? My best recommendation would be to do so, then use a high quality silicone caulk to replace it with. You should eliminate the problem this way.