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Optimal Hospital Care Scheduling During the SARS-CoV-2 Pandemic

Josh D’Aeth(j.daeth17***at***imperial.ac.uk)
Shubhechyya Ghosal(s.ghosal16***at***imperial.ac.uk)
Fiona Grimm(Fiona.Grimm***at***health.org.uk)
David Haw(d.haw***at***imperial.ac.uk)
Esma Koca(e.koca13***at***imperial.ac.uk)
Krystal Lau(k.lau15***at***imperial.ac.uk)
Huikang Liu(hkliu2014***at***gmail.com)
Stefano Moret(s.moret***at***imperial.ac.uk)
Dheeya Rizmie(dheeya.rizmie14***at***imperial.ac.uk)
Peter Smith(peter.smith***at***imperial.ac.uk)
Giovanni Forchini(g.forchini***at***imperial.ac.uk)
Marisa Miraldo(m.miraldo***at***imperial.ac.uk)
Wolfram Wiesemann(ww***at***imperial.ac.uk)

Abstract: The COVID-19 pandemic has seen dramatic demand surges for hospital care that have placed a severe strain on health systems worldwide. As a result, policy makers are faced with the challenge of managing scarce hospital capacity so as to reduce the backlog of non-COVID patients whilst maintaining the ability to respond to any potential future increases in demand for COVID care. In this paper, we propose a nation-wide prioritization scheme that models each individual patient as a dynamic program whose states encode the patient’s health and treatment condition, whose actions describe the available treatment options, whose transition probabilities characterize the stochastic evolution of the patient’s health and whose rewards encode the contribution to the overall objectives of the health system. The individual patients’ dynamic programs are coupled through constraints on the available resources, such as hospital beds, doctors and nurses. We show that near-optimal solutions to the emerging weakly coupled counting dynamic program can be found through a fluid approximation that gives rise to a linear program whose size grows gracefully in the problem dimensions. Our case study for the National Health Service in England shows how years of life can be gained and costs reduced by prioritizing specific disease types over COVID patients, such as injury & poisoning, diseases of the respiratory system, diseases of the circulatory system, diseases of the digestive system and cancer.

Keywords: COVID, Care Prioritization, Weakly Coupled Counting Dynamic Programs, Fluid Approximation

Category 1: Applications -- OR and Management Sciences (Other )

Category 2: Other Topics (Dynamic Programming )

Category 3: Stochastic Programming

Citation: Imperial College London and Umea University

Download: [PDF]

Entry Submitted: 02/23/2021
Entry Accepted: 02/23/2021
Entry Last Modified: 02/23/2021

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