Well for one thing, it certainly couldn't have been HIV. That is a 21st century disease.
As for the in-depth discussion during that section of the bible (as I've read this part!) it details a whole host of skin diseases. Yes, "leprosy" was used as a general term because they didn't have names for everything yet, however actual leprosy is a disease and was one of the things they watched for.
It is possible that HPV was included, but something like syphillus could not have been since its symptoms are mental and not as physical.
YES, you *are* capable of carrying some of these diseases dormant
after catching them. In other words, they don't pass down genetically. You can't get them from your parents.