Probably have you a while ago suffered through acute rhinitis? Conceivably did you heal from the infection? Obviously you recovered! You won't cure a runny nose itself, but your immune system usually develops immunity to any type of cold virus within a couple of weeks. We call that being cured by your personal immune system!
HPV is similar in that HPV is just an additional infection. And you could most likely establish immunity to HPV. Nevertheless, HPV is more capable at evading your body's immune system compared to the rhinitis viruses. So you have to try a little harder to obtain resistance to human papilloma virus.
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