Spatio-temporal disease mapping models are a popular tool to describe the pattern of disease counts. They are
usually formulated in a hierarchical Bayesian framework with latent Gaussian model. So far, computationally expensive Markov chain Monte Carlo algorithms have been used for parameter estimation which might induce a large
Monte Carlo error. An alternative method using integrated nested Laplace approximations (INLA) has recently been
proposed. A major advantage of INLA is that it returns accurate parameter estimates in short computational time.
Additionally, the deviance information criterion is provided for Bayesian model choice. This paper describes how several parametric and nonparametric models and extensions thereof can be fitted to space–time count data using INLA. Particular emphasis is given to the appropriate choice of linear constraints to ensure identifiability of the parameter estimates. The models are applied to counts of Salmonellosis in cattle reported to the Swiss Federal Veterinary Office 1991–2008.