[arahant]

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First - cervical cancer is effectively contagious to the extent it is viral in origin. There is no rationale for distinguishing between the cancer itself and the virus in this case.

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No. You're assuming a lot of things that aren't true. First, that all cases of the cancer are caused by HPV, second, that the relevant HPV strains always result in cancer, third that there is no useful general distinction between the virus and the cancer it eventually causes (should we not distinguish between HIV and AIDS, either?), and finally that treatment doesn't differ between the cancer and the virus.

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I didn't assume any of those things. "effectively" and "to the extent" encompass your caveats. For the purpose of this analysis, we can treat some subset of cervical cancers as contagious, and preventable by the vaccine. The distinctions you make are just about the numbers that go into the cost benefit analysis. Obviously your caveats are all true.