Impact of prophylactic vaccination against human papillomavirus infection

Human papillornavirus (HPV) is the primary cause of cervical carcinoma and its precursor lesions. Prophylactic vaccines against oncogenic and warts-causing genital HPV types are currently under development and are expected to be available in the near future. This paper presents a two-sex, deterministic model for assessing the potential impact of a prophylactic HPV vaccine that has five biological modes of action: "take", "degree", "duration", "infectiousness", and "clearance". The model is based on the susceptible-infective-removed (SIR) compartmental structure. Important epidemiological thresholds such as the basic and vaccinated reproduction numbers and a measure of vaccine impact are derived. We find that if the vaccinated reproduction number is greater than unity, there is a locally unstable disease-free equilibrium and a unique endemic equilibrium. If the vaccinated reproduction number is less than unity, HPV will be eliminated. We use analytical and numerical methods to analyze the importance of various vaccine efficacy parameters as well as compare gender-specific and universal vaccination.