Human Papillomavirus is the most frequent sexually transmitted infection. Human Papillomavirus (HPV) is the primary cause of cervical cancer and its precursor lesions. Two prophylactic vaccines against HPV infections are available. Mathematical models can be used to compare several vaccine strategies. Consequently, most effective vaccine strategy can be enlightened and selected. Nevertheless, proposed HPV transmission models in the litterature have become very complex while some input values remain unknown or badly estimated. Our aim was to assess the variability in the outcome variable that is due to the uncertainty in estimating the input values. We carried out and calibrated a Susceptible-Infected-Susceptible model of heterosexual transmission of Human Papillomavirus infections for serotypes 6/11/16/18 which are covered by the quadrivalent vaccine. Immunity obtained from vaccination was considered. The basic and vaccinated basic reproduction numbers were expressed. Model prediction sensitivity to parameters uncertainty has been assessed using the Partial Rank Correlation Coefficients. Three scenarios of vaccination have been compared considering estimated HPV infection prevalences. Six posterior parameter sets among one million combination tested best fitted epidemiologic data. Sensitivity analysis showed that the significiance level of uncertainty was linked to the length of different serotype HPV infections in model predictions. Deterministic modeling of HPV infection transmission allowed us to compare potential efficiency of 3 vaccination scenarios. Additional vaccination of the half of men who enter annually in the sexually active population led to the same results when compared to an exclusive large vaccination rate of women (who enter annually in the sexually active population). Sensitivity analysis showed the importance of clearance rate in the precision of model predictions, therefore efforts have to been made to focus data collection concerning duration of HPV infections. Furthermore, usefulness of men's vaccination depends on women's vaccination rate.