Ideas on how to prevent mildew and clean it around kitchen sink?

remodeled kitchen 2 years ago and now mildew is building up on sink edge where the caulk was installed. starts out with light black spots and beginning to turn solid black color. it's an undermount sink (white porcelen with granite top). i hate to hire someone to scrap all of the caulking out and install new caulk. afraid it'll start all over again. thanks for your suggestions