Possibly have you ever had a cold virus? Probably did you recover from the issue? Certainly you got over it! You can not cure a runny nose itself, but your system normally establishes immunity to any type of cold infection within a couple of days. We call that cured by your personal immune system!

HPV virus is the same because human papilloma virus is just one more infection. Therefore you can normally create immunity to HPV. However, human papilloma virus is more adept at concealing from your immune system compared to the cold virus viruses. Therefore you should try harder to develop resistance to HPV virus.
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