Cervical cancer is the fourth most common malignancy in women worldwide, although it is preventable with prophylactic HPV vaccination. HPV transmission-dynamic models can predict the potential for global elimination of cervical cancer. The random network model is a new approach that allows individuals to be followed, and to implement a given vaccination policy according to their clinical records. We developed an HPV transmission dynamics model on a lifetime sexual partners network based on individual contacts, also accounting for the sexual behavior of men who have sex with men (MSM). We analyzed the decline in the prevalence of HPV infection in a scenario of 75% and 90% coverage for both sexes. An important herd immunity effect for men and women was observed in the heterosexual network, even with 75% coverage. However, HPV in-fections are persistent in the MSM population, with sustained circulation of the virus among un-vaccinated individuals. Coverage around 75% of both sexes would be necessary to eradicate HPV-related conditions in women within five decades. Nevertheless, the variation in the decline in infection in the long term between vaccination coverage of 75% and 90% is relatively small, suggesting that reaching coverage of around 70-75% in the heterosexual network may be enough to confer high protection. Nevertheless, HPV eradication maybe achieved if men’s coverage is strictly controlled. This accurate representation of HPV transmission demonstrates the need to maintain high HPV vaccination coverage, especially in men, for whom the cost-effectiveness of vaccination is questioned.