Bayesian temporal, spatial and spatio-temporal models of dengue in a small area with INLA

Understanding spatio-temporal patterns of communicable diseases and their dependency structure is crucial for assessing the potential mitigation and control measures. This paper presents various Bayesian models of dengue and studies the models with Integrated Nested Laplace Approximation (INLA) approach. Several structure models, as the combination of two temporal models of Autoregressive (AR) and Random Walk (RW), and three likelihoods of Gaussian, Poisson and Negative Binomial, are developed and utilised. The study further formulates a spatial model and four types of spatio-temporal models, as the combination of spatial and temporal random effects. All proposed models are applied to the dengue counts in the small city of Kendari, Indonesia. Based on the DIC and WAIC values, the level counts of dengue for each county are well described by AR(1)-Poisson. The best performances of the single-trend model and the multiple-trend model are achieved with AR(1)-Negative Binomial and AR(2)-Poisson, respectively. The multiple-trend model performs better than the single-trend model. Both spatial and spatiotemporal models show a significant spatial and temporal impact on the area-specific relative risk. The spatio-temporal model of Type I performs better than the other types on the dengue dataset, and followed by Type IV as the second best model.