Running a UV 24/7 will prevent the transmission of pathogens. Therefore if you do something unwise and introduce a pathogen, often times only the orignal infected fish will contract the disease. Remember though, as a vertebrate, a fish's immune system is not drastically different from ours. It's capacity to fight infection is generated from contact with the pathogen, so it's chicken or the egg... Kill the pathogen before it contacts the fish, thus it never gets the antibodies, or allow it to contact the pathogen, make the antibodies and get a remembered immune response...
I personally run it 24/7 both to prevent disease transmission, AND to lessen algae growth. FWIW when I had a clean, FUNCTIONING UV sterilizer running I've never had a transmission of disease from one fish to another. The one time I had an ich outbreak jumping from fish to fish, I found out (too late) that the lense in the unit was covered in gunk, making it non-functional. Lost 2 new introductions to disease since then with a clean UV sterilizer and the disease was NOT transmitted to other fish. Take that FWIW