Infectious diseases both within human and animal populations often pose serious health and socioeconomic risks. From a statistical perspective, their prediction is complicated by the fact that no two epidemics are identical due to changing contact habits, mutations of infectious agents, and changing human and animal behaviour in response to the presence of an epidemic. Thus model param-
eters governing infectious mechanisms will typically be unknown. On the other
hand, epidemic control strategies need to be decided rapidly as data accumulate.
In this paper we present a fully Bayesian methodology for performing inference
and online prediction for epidemics in structured populations. Key features of
our approach are the development of an MCMC- (and adaptive MCMC-) based
methodology for parameter estimation, epidemic prediction, and online assessment of risk from currently unobserved infections. We illustrate our methods using two complementary studies: an analysis of the 2001 UK Foot and Mouth epidemic, and modelling the potential risk from a possible future Avian Influenza epidemic to the UK Poultry industry.