  In this chapter, we consider space-time analysis of surveillance count data.
Such data are ubiquitous and a number of approaches have been proposed for
their analysis. We first describe the aims of a surveillance endeavor, before
reviewing and critiquing a number of common models. We focus on models in which
time is discretized to the time scale of the latent and infectious periods of
the disease under study. In particular, we focus on the time series SIR (TSIR)
models originally described by Finkenstadt and Grenfell in their 2000 paper and
the epidemic/endemic models first proposed by Held, Hohle, and Hofmann in their
2005 paper. We implement both of these models in the Stan software and
illustrate their performance via analyses of measles data collected over a
2-year period in 17 regions in the Weser-Ems region of Lower Saxony, Germany.
