Abstinence may be effective in the ideal, but teaching abstinence in the real world has not been shown to reduce STI or pregnancy rates repeatably for more than a few months.
The current HPV vaccine, on the other hand, has been shown to reduce CIN3 by about 50% in 20-21 year olds; see http://www.ncbi.nlm.nih.gov/pubmed/25180766
Now, abstinence *enforced by law* might work; it probably does work in highly repressive countries. But that's not an approach DeMedio would seriously advocate. Stoning also went out with the Vikings.
We won't have to wait 40 years to see whether the vaccines prevent cervical cancer. Lehtinen writes in http://www.future-science.com/doi/pdf/10.4155/cli.12.143 "We have ≥80%
power to provide data on vaccine efficacy against CIN3
in 2014, against ICC in 2022 and against other HPVassociated
cancers in 2024".