Inference of type-specific HPV transmissibility, progression and clearance rates: a mathematical modelling approach.

Quantifying rates governing the clearance of Human Papillomavirus (HPV) and its progression to clinical disease, together with viral transmissibility and the duration of naturally-acquired immunity, is essential in estimating the impact of vaccination programmes and screening or testing regimes. However, the complex natural history of HPV makes this difficult. We infer the viral transmissibility, rate of waning natural immunity and rates of progression and clearance of infection of 13 high-risk and 2 non-oncogenic HPV types, making use of a number of rich datasets from Sweden. Estimates of viral transmissibility, clearance of initial infection and waning immunity were derived in a Bayesian framework by fitting a susceptible-infectious-recovered-susceptible (SIRS) transmission model to age- and type-specific HPV prevalence data from both a cross-sectional study and a randomised controlled trial (RCT) of primary HPV screening. The models fitted well, but over-estimated the prevalence of four high-risk types with respect to the data. Three of these types (HPV-33, -35 and -58) are among the most closely related phylogenetically to the most prevalent HPV-16. The fourth (HPV-45) is the most closely related to HPV-18; the second most prevalent type. We suggest that this may be an indicator of cross-immunity. Rates of progression and clearance of clinical lesions were additionally estimated from longitudinal data gathered as part of the same RCT. Our estimates of progression and clearance rates are consistent with the findings of survival analysis studies and we extend the literature by estimating progression and clearance rates for non-16 and non-18 high-risk types. We anticipate that such type-specific estimates will be useful in the parameterisation of further models and in developing our understanding of HPV natural history.