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

TL;DR

This paper introduces a cellular automaton model based on the Abelian Sandpile paradigm to optimize patient redistribution among hospitals during COVID-19, aiming to prevent healthcare system collapse.

Contribution

It develops a novel mathematical model applying Self-Organised Criticality to hospital resource management during pandemics.

Findings

The model effectively reduces hospital overloads.

It outperforms standard management strategies.

The indicator function measures allocation efficiency.

Abstract

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.