  More than half of the world's population is exposed to the risk of
mosquito-borne diseases, which leads to millions of cases and hundreds of
thousands of deaths every year. Analyzing this type of data is often complex
and poses several interesting challenges, mainly due to the vast geographic
area, the peculiar temporal behavior, and the potential correlation between
infections. Motivation stems from the analysis of tropical diseases data,
namely, the number of cases of two arboviruses, dengue and chikungunya,
transmitted by the same mosquito, for all the 145 microregions in Southeast
Brazil from 2018 to 2022. As a contribution to the literature on multivariate
disease data, we develop a flexible Bayesian multivariate spatio-temporal model
where temporal dependence is defined for areal clusters. The model features a
prior distribution for the random partition of areal data that incorporates
neighboring information, thus encouraging maps with few contiguous clusters and
discouraging clusters with disconnected areas. The model also incorporates an
autoregressive structure and terms related to seasonal patterns into temporal
components that are disease and cluster-specific. It also considers a
multivariate directed acyclic graph autoregressive structure to accommodate
spatial and inter-disease dependence, facilitating the interpretation of
spatial correlation. We explore properties of the model by way of simulation
studies and show results that prove our proposal compares well to competing
alternatives. Finally, we apply the model to the motivating dataset with a
twofold goal: clustering areas where the temporal trend of certain diseases are
similar, and exploring the potential existence of temporal and/or spatial
correlation between two diseases transmitted by the same mosquito.
