  We consider an epidemic spreading in a city which is divided geographically
into different districts. We introduce the reproduction matrix
$\R=\bigl(R(i,j)\bigr)$ between districts, where $R(i,j)$ is the mean number of
individuals in district $j$ infected by an individual from district $i$. We
analyse policies of partial lockdowns of the city, that is of a set of
districts, based on the study of matrix $\R$, where rows and columns
corresponding to districts in lockdown are set to zero. This schema can also be
applied to a country divided into regions or other appropriate units, provided
the relevant information is available. We conclude by analyzing a matrix~$\R$
which was constructed for the spread of COVID-19 in Santiago, Chile, with the
aid of an agent-based simulator for generating surrogate district data.
