Cervical cancer deaths have dropped by around 80% in the US due to mass Pap smear screening. Prior to the 50's it was the second leading cause of cancer death among American women, topped only by breast cancer.
The same can happen here with this shot. Making it mandatory is STUPID. Besides it's unconstitutional to FORCE anyone to have a shot, especially for a std that MAY develop into cancer. In fact, most of the time it DOESN'T, and goes away on it's own, natually via your own immune system.