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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.