Herd immunity effect of the HPV vaccination program in Australia under different assumptions regarding natural immunity against re-infection.

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.

Adaptive Markov chain Monte Carlo forward projection for statistical analysis in epidemic modelling of human papillomavirus.

A Bayesian statistical model and estimation methodology based on forward projection adaptive Markov chain Monte Carlo is developed in order to perform the calibration of a high-dimensional nonlinear system of ordinary differential equations representing an epidemic model for human papillomavirus types 6 and 11 (HPV-6, HPV-11). The model is compartmental and involves stratification by age, gender and sexual-activity group. Developing this model and a means to calibrate it efficiently is relevant because HPV is a very multi-typed and common sexually transmitted infection with more than 100 types currently known. The two types studied in this paper, types 6 and 11, are causing about 90% of anogenital warts. We extend the development of a sexual mixing matrix on the basis of a formulation first suggested by Garnett and Anderson, frequently used to model sexually transmitted infections. In particular, we consider a stochastic mixing matrix framework that allows us to jointly estimate unknown attributes and parameters of the mixing matrix along with the parameters involved in the calibration of the HPV epidemic model. This matrix describes the sexual interactions between members of the population under study and relies on several quantities that are a priori unknown. The Bayesian model developed allows one to estimate jointly the HPV-6 and HPV-11 epidemic model parameters as well as unknown sexual mixing matrix parameters related to assortativity. Finally, we explore the ability of an extension to the class of adaptive Markov chain Monte Carlo algorithms to incorporate a forward projection strategy for the ordinary differential equation state trajectories. Efficient exploration of the Bayesian posterior distribution developed for the ordinary differential equation parameters provides a challenge for any Markov chain sampling methodology, hence the interest in adaptive Markov chain methods. We conclude with simulation studies on synthetic and recent actual data.