Bayesian modeling of spatial integer-valued time series

Many infectious diseases spread through person-to-person contact, either directly or indirectly. The proposal incorporates spatial-temporal patterns into multivariate integer-valued GARCH models with either a generalized Poisson distribution or zero-inflated generalized Poisson distribution in order to describe these features of the data. By considering the neighboring locations of the target series, the set-up incorporates a flexible and continuous conceptualization of distance to present the spatial components, thereby highlighting for the non-separability of space and time. Such an approach eliminates the need to pre-assign a spatial weight matrix. Newly designed models are utilized to investigate time-series counts of infectious diseases, enabling inference, prediction, and model selection within a Bayesian framework through Markov chain Monte Carlo (MCMC) algorithms. As an illustration, design simulation studies and multivariate weekly dengue cases are scrutinized for the performance of the Bayesian methods. The proposed models successfully capture the characteristics of spatial dependency, over-dispersion, and a large portion of zeros, providing a comprehensive model for the observed phenomena in the data.