  The emergence of Covid-19 requires new effective tools for epidemiological
surveillance. Spatio-temporal disease mapping models, which allow dealing with
highly disaggregated spatial and temporal units of analysis, are a priority in
this sense. Spatio-temporal models provide a geographically detailed and
temporally updated overview of the current state of the pandemics, making
public health interventions to be more effective. Moreover, the use of
spatio-temporal disease mapping models in the new Covid-19 epidemic context,
facilitates estimating newly demanded epidemiological indicators, such as the
instantaneous reproduction number (R_t), even for small areas. This, in turn,
allows to adapt traditional disease mapping models to these new circumstancies
and make their results more useful in this particular context.
  In this paper we propose a new spatio-temporal disease mapping model,
particularly suited to Covid-19 surveillance. As an additional result, we
derive instantaneous reproduction number estimates for small areas, enabling
monitoring this parameter with a high spatial disaggregation. We illustrate the
use of our proposal with the separate study of the disease pandemics in two
Spanish regions. As a result, we illustrate how touristic flows could haved
shaped the spatial distribution of the disease. In these real studies, we also
propose new surveillance tools that can be used by regional public health
services to make a more efficient use of their resources.
