Dynamic fair balancing of COVID-19 patients over hospitals based on forecasts of bed occupancy

This paper introduces mathematical models that support dynamic fair balancing of COVID-19 patients over hospitals in a region and across regions. Patient flow is captured in an infinite server queueing network. The dynamic fair balancing model within a region is a load balancing model incorporating a forecast of the bed occupancy, while across regions, it is a stochastic program taking into account scenarios of the future bed surpluses or shortages. Our dynamic fair balancing models yield decision rules for patient allocation to hospitals within the region and reallocation across regions based on safety levels and forecast bed surplus or bed shortage for each hospital or region. Input for the model is an accurate real-time forecast of the number of COVID-19 patients hospitalised in the ward and the Intensive Care Unit (ICU) of the hospitals based on the predicted inflow of patients, their Length of Stay and patient transfer probabilities among ward and ICU. The required data is obtained from the hospitals' data warehouses and regional infection data as recorded in the Netherlands. The algorithm is evaluated in Dutch regions for allocation of COVID-19 patients to hospitals within the region and reallocation across regions using data from the second COVID-19 peak.