You’re right. It could have been more nuanced about the HPV eradication. Still, if only 1/1000 cervical cancers have other etiologies, that does take them out of the most common cancers and make them rare. As a broad public health concern, it will be pretty close to eradicated.

And yes, no cancer can be eradicated, ever. Life finds a way.

0.1% is pretty good as far as headline exaggerations go.

HPV can actually cause other cancers besides just cervical.

https://www.cdc.gov/hpv/parents/cancer.html

>HPV cancers include cancer of the cervix, vulva, vagina, penis, or anus. HPV infection can also cause cancer in the back of the throat, including the base of the tongue and tonsils (called oropharyngeal cancer).

Because we tend to classify cancers by which organ was affected, _technically_ eradicating cervical cancer isn't possible without getting rid of the cervix (which you can technically do, but it's major surgery).

However, practically all cervical cancer is caused by HPV. Without HPV cervical cancer would be extremely rare, because it's going to need several quite uncommon random events to coincide, the virus is "deliberately" meddling with the copying mechanics inside cells, that's how a virus propagates, without a virus those changes have to happen entirely by accident, maybe a series of cosmic rays.

So it's not _that_ hyperbolic to say this eradicates the cancer itself.