Periodicity of varicella-zoster virus in the presence of immune boosting and clinical reinfection with varicella.

BACKGROUND: Clinical reinfection with varicella is normally ignored in mathematical transmission models as it is considered too rare to be important. METHODS: We apply basic bifurcation analysis to a simple mathematical model of varicella-zoster virus (VZV) transmission incorporating reinfection. RESULTS: We demonstrate that under certain conditions this model can exhibit periodic behaviour as opposed to what is observed in VZV models that ignore the possibility of repeat varicella attacks. Periodicity can be induced by a combination of immune boosting and reinfection while the impact of zoster (shingles) recurrence on the onset of periodicity is negligible. CONCLUSIONS: Our results suggest that mathematical models of VZV may benefit from inclusion of repeat varicella.

The potential impact of HPV-16 reactivation on prevalence in older Australians.

BACKGROUND: Some regional cross-sectional human papillomavirus (HPV) DNA prevalence data show an increase in prevalence in older women, the reasons for which are as yet unknown. A recently published study suggests that the increase may be at least partly due to reactivation of latent HPV in menopausal women. METHODS: We developed a dynamic mathematical model of HPV-16 transmission to estimate the key consequences of hypothetical HPV-16 reactivation in the Australian heterosexual population. We only consider a worst case scenario with regard to reactivation in the Australian setting when all women who are latently infected reactivate and, wherever feasible, we choose model parameter values which may lead to a more pronounced reactivation. The ongoing National HPV vaccination program covering both women and men is incorporated in the model. RESULTS: We estimate that about 1 in 10 women and men who appear to have cleared HPV-16 infection may be latently infected. The prevalence of HPV-16 in older Australian women will increase by a factor of up to 3.1 between now and 2025 which will be accompanied by an increase by a factor of around 1.9 in older men. However, the long-term impact of the HPV vaccination is not significantly altered by reactivation. CONCLUSIONS: If the reactivation hypothesis we consider is substantiated, the public health response should be focused on further improvement of cervical screening coverage for older women. Our study also highlights the urgent need for surveillance of HPV prevalence in older Australians.

Near elimination of genital warts in Australia predicted with extension of human papillomavirus vaccination to males.

BACKGROUND: The National Human Papillomavirus (HPV) Vaccination Program for females delivering the quadrivalent vaccine Gardasil has been included in the National Immunisation Program in Australia since 2007. Sentinel surveillance data show that genital wart incidence has been steadily declining since then. The objective of this study was to estimate the additional impact on genital warts as a result of male vaccination, which was approved by the Australian government in 2012 and commenced in 2013. METHODS: We use a mathematical model of HPV transmission in the Australian heterosexual population to predict the impact of male vaccination on the incidence of genital warts. RESULTS: Our model produced results that are consistent with the actual observed decline in genital warts and predicted a much lower incidence, approaching elimination, in coming decades with the introduction of male vaccination. CONCLUSIONS: Results from our model indicate that the planned extension of the National HPV Vaccination Program to males will lead to the near elimination of genital warts in both the female and male heterosexual populations in Australia.

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.

The association of HPV-16 seropositivity and natural immunity to reinfection: insights from compartmental models.

BACKGROUND: Seroreactivity, processes of seroconversion and seroreversion, in the context of HPV infection has been investigated in numerous studies. However, the data resulting from these studies are usually not accounted for in mathematical transmission models of various HPV types due to gaps in our understanding of the nature of seroreactivity and its implications for HPV natural history. METHODS: In this study we selected a number of simple but plausible compartmental transmission models of HPV-16, differing in assumptions regarding the relation between seropositivity and immunity, and attempted to calibrate them to Australian HPV seroprevalence data for females and males, as well as DNA prevalence data for females, using a Bayesian model comparison procedure. We ranked the models according to both their simplicity and ability to be fitted to the data. RESULTS: Our results demonstrate that models with seroreversion where seropositivity indicates only a partial or very short-term full protection against re-infection generate age-specific HPV DNA prevalence most consistent with the observed data when compared with other models. CONCLUSIONS: Models supporting the notion that seropositive individuals are fully immune to reinfection demonstrated consistently inferior fits to the data than other models making no such assumption.

Varicella-Zoster Virus in Perth, Western Australia: Seasonality and Reactivation.

BACKGROUND: Identification of the factors affecting reactivation of varicella-zoster virus (VZV) largely remains an open question. Exposure to solar ultra violet (UV) radiation is speculated to facilitate reactivation. Should the role of UV in reactivation be significant, VZV reactivation patterns would generally be expected to be synchronous with seasonal UV profiles in temperate climates. METHODS: We analysed age and gender specific VZV notification time series data from Perth, Western Australia (WA). This city has more daily sunshine hours than any other major Australian city. Using the cosinor and generalized linear models, we tested these data for seasonality and correlation with UV and temperature. RESULTS: We established significant seasonality of varicella notifications and showed that while herpes-zoster (HZ) was not seasonal it had a more stable seasonal component in males over 60 than in any other subpopulation tested. We also detected significant association between HZ notifications and UV for the entire Perth population as well as for females and males separately. In most cases, temperature proved to be a significant factor as well. CONCLUSIONS: Our findings suggest that UV radiation may be important for VZV reactivation, under the assumption that notification data represent an acceptably accurate qualitative measure of true VZV incidence.

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.