Published Online:

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 to reduce the backlog of non-COVID patients while maintaining the ability to respond to any potential future increases in demand for COVID care. In this paper, we propose a nationwide 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 the overall problem can be modeled as a grouped weakly coupled dynamic program for which we determine near-optimal solutions through a fluid approximation. Our case study for the National Health Service in England shows how years of life can be gained by prioritizing specific disease types over COVID patients, such as injury and poisoning, diseases of the respiratory system, diseases of the circulatory system, diseases of the digestive system, and cancer.

This paper was accepted by Chung-Piaw Teo, optimization.

Funding: G. Forchini acknowledges funding from Jan Wallanders and Tom Hedelius Foundation and the Tore Browaldh Foundation, funding from MRC Centre for Global Infectious Disease Analysis [Reference MR/R015600/1], jointly funded by the UK Medical Research Council (MRC) and the UK Foreign, Commonwealth and Development Office (FCDO), under the MRC/FCDO Concordat agreement, part of the EDCTP2 program supported by the European Union; and acknowledges funding by Community Jameel. D. Rizmie acknowledges partial funding from the MRC Centre for Global Infectious Disease Analysis [Reference MR/R015600/1]. J. C. D’Aeth acknowledges funding from the Wellcome Trust [Reference 102169/Z/13/Z]. S. Moret acknowledges partial support from the Swiss National Science Foundation (SNSF) under [Grant P2ELP2_188028]. S. Ghosal was funded by the Imperial College President’s PhD Scholarship. F. Grimm was funded by the Health Foundation as part of core staff member activity. This research was funded in whole, or in part, by the Wellcome Trust [Grant 102169/Z/13/Z].

Supplemental Material: The data files are available at

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