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

Hospital management in the COVID-19 emergency: Abelian Sandpile paradigm and beyond