  Epidemics are often modelled 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 MCMC 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 SEIR-type models with age structure are also introduced.
