Cervical cancer (CC) is the second leading cause of cancer-related deaths among Colombian women, caused most commonly by Human Papillomavirus (HPV) infection. Screening programs, vaccination against HPV and improved socio-economic conditions have significantly reduced CC mortality rate over the last 40 years. Understanding the transmission dynamics of HPV infection is essential to the definition of cost-effective disease control strategies. We propose a compartmentalized epidemiological simulation model based on differential equations, which represents HPV transmission within the population, likelihood of infection clearance, virus induced appearance of precancerous lesions and eventually of CC. Time-dependent birth and natural mortality rates inferred from census are used to calibrate model population dynamics. Literature data and 5-years medical records of 3,428 Colombian women are used to estimate the infection dynamics and cancerous stages. The model allows evaluating the predicted effects of vaccination strategies against HPV, providing valuable support to healthcare decision-makers.