Here in Canada, there has long been a ban in importing and growing Japanese Barberries. Rain, overhead watering and wind spread rust. Some rusts pass their lives on a single host, while others require two or more hosts to complete their life cycle, such as pear trellis rust which summers on Pears and winters on Junipers. Never grow Pears near Junipers. Rusts utilize their hosts in many ways, but it is always aggravated by humidity on the leaves.
Prevention Be sure to clean up dead leaves around the plants.
Garden Sulphur is also a very good spray to use on all kinds of fungus and mildew type of things in the garden. It smells like rotten eggs but it does alot of good and is approved as an organic product for organic growers. Mint often grows on lush new growth, and sometimes overfertilization can take an already-present rust situation and make it worse. Plants with too many new leaves are more succeptible than those grown on a lean diet. Never top-dress mint with manure, and keep feedings to a minimum.