  In this article, we propose a mathematical model -- based on a cellular
automaton -- for the redistribution of patients within a network of hospitals
with limited available resources, in order to reduce the risks of a
local/global collapse of the healthcare system. We attempt at developing a
conceptual tool to support making rational decisions relevant to the
optimisation of the allocation of patients into accessible medical facilities.
The strategy is based on a version of the Abelian Sandpile model for the
Self-Organised Criticality, with the idea of testing the paradigm for the
management of patients among the COVID-19 hospitals in Italian regions. In
particular, we compare the novel proposal to the standard management of
connections between hospitals, showing a number of advantages at a local and
global level, by means of a reliable indicator function introduced for
measuring the effectiveness of the allocation strategies.
