Optimizing Inter-Hospital Patient Transfer Decisions During a Pandemic : A Queueing Network Approach

Problem definition: Geographical mismatch between demand for care and availability of healthcare resources has been a major challenge during the COVID-19 pandemic. As such, inter-hospital patient transfers have emerged as a key aspect of the pandemic response in many countries. We propose and investigate inter-facility patient transfer policies with the goal of alleviating hospital congestion and reducing inequities in the distribution of COVID patients across the health system. Methodology/Results: We propose a queueing network model that captures the salient features of patient flow from acute wards to ICUs within each hospital, and between wards and ICUs of different hospitals in a network. We formulate the problem of determining optimal patient transfer policies between the hospitals as a stochastic control problem and develop a solution method by leveraging a deterministic fluid approximation of the queueing network. Using real data during the pandemic from a network of 21 hospitals in the Greater Toronto Area of Ontario, Canada, we validate our queueing model and conduct a comprehensive case study to examine the value of guiding patient transfers using our proposed approach. Compared to the no-transfer policy, the expected reduction in the number of patient days above a 95% occupancy threshold under our policy can be up to 43.6% in wards and 30.9% in ICUs, and the expected reduction in COVID load inequity can be up to 53.2%. In addition, we find that our optimized transfers outperform the actual transfer decisions made during the periods considered in the case study. Managerial implications: Guiding patient transfers using our proposed approach can be effective in alleviating congestion imbalances and reducing inequities during pandemics or other episodes of surge in hospitalizations (e.g., flu season). These benefits could be realized using a relatively small number of daily transfers