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Adaptive Markov Chain Monte Carlo Forward Simulation for Statistical Analysis in Epidemic Modelling of Human Papillomavirus

We develop a Bayesian statistical model and estimation methodology based on Forward Projection Adaptive Markov chain Monte Carlo in order to perform the calibration of a high-dimensional non-linear 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 since 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 for the population, based on a formulation first suggested by Garnett and Anderson. In particular we consider a stochastic mixing matrix framework which 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 which are a-priori unknown. The Bayesian model developed allows one to estimate jointly the HPV-6 and HPV-11 epidemic model parameters such as the probability of transmission, HPV incubation period, duration of infection, duration of genital warts treatment, duration of immunity, the probability of seroconversion, per gender, age-group and sexual activity-group, as well as unknown sexual mixing matrix parameters related to assortativity. We conclude with simulation studies on synthetic and actual data from studies undertaken recently in Australia.