We model the incidence of the COVID-19 disease during the first wave of the epidemic
in Castilla-Leon (Spain). Within-province dynamics may be governed by a generalized logistic
map, but this lacks of spatial structure. To couple the provinces, we relate the daily new infec-
tions through a density-independent parameter that entails positive spatial correlation. Pointwise
values of the input parameters are fitted by an optimization procedure. To accommodate the
significant variability in the daily data, with abruptly increasing and decreasing magnitudes, a
random noise is incorporated into the model, whose parameters are calibrated by maximum like-
lihood estimation. The calculated paths of the stochastic response and the probabilistic regions
are in good agreement with the data
