title: Capturing the time-varying drivers of an epidemic using stochastic dynamical systems.
abstract: Epidemics are often modeled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions, seasonal effects, etc.). These models assign diffusion processes to the time-varying parameters, and our inferential procedure is based on a suitably adjusted adaptive particle Markov chain Monte Carlo algorithm. The performance of the proposed computational methods is validated on simulated data and the adopted model is applied to the 2009 H1N1 pandemic in England. In addition to estimating the effective contact rate trajectories, the methodology is applied in real time to provide evidence in related public health decisions. Diffusion-driven susceptible exposed infected retired-type models with age structure are also introduced.
authors.affiliation: Department of Statistics, London School of Economics and Political Science, London WC2A 2AE, UK. j.dureau@lse.ac.uk
authors.forename: Joseph
authors.initials: J
authors.lastname: Dureau
authors.forename: Konstantinos
authors.initials: K
authors.lastname: Kalogeropoulos
authors.forename: Marc
authors.initials: M
authors.lastname: Baguelin
mesh_terms: D000328:Adult; D000465:Algorithms; D001499:Bayes Theorem; D056808:Biostatistics; D002648:Child; D004739:England / Q000453:epidemiology; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D053118:Influenza A Virus, H1N1 Subtype; D007251:Influenza, Human / Q000453:epidemiology; D008390:Markov Chains; D008954:Models, Biological; D015233:Models, Statistical; D009010:Monte Carlo Method; D017711:Nonlinear Dynamics; D058873:Pandemics / Q000706:statistics & numerical data; D013269:Stochastic Processes; D013997:Time Factors
keywords: Bayesian inference; Particle MCMC; Population epidemic model; Time-varying parameters