Spatio-temporal hierarchical modeling of an infectious disease from (simulated) count data
An infectious disease spreads through "contact" between an individual who has the disease and one who does not. However, modeling the individual-level mechanism directly requires data that would amount to observing (imperfectly) all individuals' disease statuses along their space-time lines in the region and time period of interest. More likely, data consist of spatio-temporal aggregations that give small-area counts of the number infected during successive, regular time intervals. In this paper, we give a spatially descriptive, temporally dynamic hierarchical model to be fitted to such data. The dynamics of infection are described by just a few parameters, which can be interpreted. We take a Bayesian approach to the analysis of these space-time count data, using Markov chain Monte Carlo to compute Bayes estimates of all parameters of interest. As a "proof of concept," we simulate data from the model and investigate how well our approach recovers important hidden features.
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