Deterministic dynamic compartmental transmission models (DDCTMs) of human papillomavirus (HPV) transmission have been used in a number of studies to estimate the potential impact of HPV vaccination programs. In most cases, the models were built under the assumption that an individual who cleared HPV infection develops (life-long) natural immunity against re-infection with the same HPV type (this is known as SIR scenario). This assumption was also made by two Australian modelling studies evaluating the impact of the National HPV Vaccination Program to assist in the health-economic assessment of male vaccination. An alternative view denying natural immunity after clearance (SIS scenario) was only presented in one study, although neither scenario has been supported by strong evidence. Some recent findings, however, provide arguments in favour of SIS. We developed HPV transmission models implementing life-time (SIR), limited, and non-existent (SIS) natural immunity. For each model we estimated the herd immunity effect of the ongoing Australian HPV vaccination program and its extension to cover males. Given the Australian setting, we aimed to clarify the extent to which the choice of model structure would influence estimation of this effect. A statistically robust and efficient calibration methodology was applied to ensure credibility of our results. We observed that for non-SIR models the herd immunity effect measured in relative reductions in HPV prevalence in the unvaccinated population was much more pronounced than for the SIR model. For example, with vaccine efficacy of 95% for females and 90% for males, the reductions for HPV-16 were 3% in females and 28% in males for the SIR model, and at least 30% (females) and 60% (males) for non-SIR models. The magnitude of these differences implies that evaluations of the impact of vaccination programs using DDCTMs should incorporate several model structures until our understanding of natural immunity is improved.
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