Did I use the word "cure"? The vaccine is to prevent an infection and the effects--cancer and genital warts, among other things. The disease is presently very widespread--men get it, too, and spread it. It can't be "cured"--but it can be mostly eliminated from the present generation of children who are not yet sexually active.
Perpetual virgins will not get the virus. But a lot of wives will get it from their husbands.