A Model of Bed Demand to Facilitate the Implementation of Data-driven Recommendations for COVID-19 Capacity Management

Background:We sought to build an accessible interactive model that could facilitate hospital capacity planning in the presence of signicant uncertainty about the proportion of the population that is positive forcoronavirus disease 2019 (COVID-19) and the rate at which COVID-19 is spreading in the population. Our goal was to facilitate the implementation of data-driven recommendations for capacity management with a transparent mathematical simulation designed to answer the specic, local questions hospital leadership considered critical. Methods:The model facilitates hospital planning with estimates of the number of Intensive Care (IC) beds, Acute Care (AC) beds, and ventilators necessary to accommodate patients who require hospitalization for COVID-19 and how these compare to the available resources. Inputs to the model include estimates of the characteristics of the patient population and hospital capacity. We deployed this model as an interactive online tool with modiable parameters. Results:The use of the model is illustrated by estimating the demand generated by COVID-19+ arrivals for a hypothetical acute care medical center. The model calculated that the number of patients requiring an IC bed would equal the number of IC beds on Day 23, the number of patients requiring a ventilator would equal the number of ventilators available on Day 27, and the number of patients requiring an AC bed and coverage by the Medicine Service would equal the capacity of the Medicine service on Day 21. The model was used to inform COVID-19 planning and decision-making, including Intensive Care Unit (ICU) stang and ventilator procurement. Conclusion:In response to the COVID-19 epidemic, hospitals must understand their current and future capacity to care for patients with severe illness. While there is signicant uncertainty around the parameters used to develop this model, the analysis is based on transparent logic and starts from observed data to provide a robust basis of projections for hospital managers. The model demonstrates the need and provides an approach to address critical questions about stang patterns for IC and AC, and equipment capacity such as ventilators.


Abstract
Background:We sought to build an accessible interactive model that could facilitate hospital capacity planning in the presence of signi cant uncertainty about the proportion of the population that is positive forcoronavirus disease 2019  and the rate at which COVID-19 is spreading in the population.
Our goal was to facilitate the implementation of data-driven recommendations for capacity management with a transparent mathematical simulation designed to answer the speci c, local questions hospital leadership considered critical. Methods:The model facilitates hospital planning with estimates of the number of Intensive Care (IC) beds, Acute Care (AC) beds, and ventilators necessary to accommodate patients who require hospitalization for COVID-19 and how these compare to the available resources. Inputs to the model include estimates of the characteristics of the patient population and hospital capacity. We deployed this model as an interactive online tool with modi able parameters. As of April 17, 2020 there have been over two million con rmed cases of coronavirus disease 2019

Results
(COVID-19) in over 180 countries, the World Health Organization characterized COVID-19 as a pandemic, and the United States (US) announced a national state of emergency. [1][2][3] In parts of China and Italy the demand for intensive care (IC) beds was higher than the number of available beds. 4,5 The limited availability of testing results in the US make it challenging to estimate the demand for hospital beds that will be generated by COVID-19 patients. We sought to build an accessible interactive model that could facilitate hospital capacity planning in the presence of signi cant uncertainty about the proportion of the population that is COVID-19 positive (COVID-19+) and the rate at which COVID-19 is spreading in the population. Our approach was to design a tool with parameters that hospital leaders could adjust to re ect their local data and easily modify to conduct sensitivity analyses. Our hypothesis was that datadriven recommendations for capacity management would be more likely to be implemented if they were presented in a transparent mathematical simulation designed to answer the speci c questions hospital leadership considered critical. 6,7 Methods: We   The model is implemented in R 3.5, RStudio, RShiny 1.4.0 and Python 3.7. The parameters used may be modi ed as data become available, for use at other institutions, and to generate sensitivity analyses.

Results:
We illustrate the use of the model by estimating the demand generated by COVID-19 + arrivals for a hypothetical acute care medical center with 100 IC beds, 220 AC beds, 75 ventilators, 80% occupancy of both IC and AC beds, 1 COVID-19 + IC patient, 2 COVID-19 + AC patients, and a total patient doubling time of 6 days. For COVID-19 + patients, 70% were assumed to stay only in AC for an average LOS of 5 days and 30% were assumed to spend at least one day in IC with an average IC LOS of 8 days and average AC LOS of 9 days (Table 1).

Model projections
The model calculated that the number of patients requiring an IC bed would equal the number of IC beds on Day 23 (Fig. 1a), the number of patients requiring a ventilator would equal the number of ventilators available on Day 27 (Fig. 1a), and the number of patients requiring an AC bed and coverage by the Medicine Service would equal the capacity of the Medicine service on Day 21 (Fig. 1b).

Sensitivity analyses
When the doubling time of new admissions is decreased to 3 days (50%), the number of days until IC and AC hit capacity decrease are, respectively, 11 and 9. When the doubling time is increased to 12 days (200%), the number of days until IC and AC hit capacity are, respectively, 51 and 51.
The model was shared publicly for use by other hospitals, and we received feedback from the model from three other institutions.

Discussion:
In response to the COVID-19 epidemic, hospitals must understand their current and future capacity to care for patients with severe illness. While there is signi cant uncertainty around the parameters used to develop this model, the analysis is based on transparent logic and starts from observed data to provide a robust basis of projections for hospital managers. The model demonstrates the need to address critical questions about sta ng patterns for IC and AC, and equipment capacity such as ventilators, and was used for decision-making in these areas at our institution within two weeks of the project start.
An insight revealed by the model is that under some plausible scenarios, AC may reach capacity before IC and become a bottleneck preventing discharges from IC. In addition to increasing capacity, managers must develop strategies to reduce AC occupancy such as accelerating efforts to discharge patients to convalescent or step-down care such as a hotel or nursing care facility.
The main limitation of this model is the fact that most of the inputs are based on estimates. The epidemiology of COVID-19 is critically important, and ongoing research will update the model. The model is very sensitive to speci c aspects of the epidemiology, especially doubling time. The model environment can be easily updated with new parameter data to generate a more precise projection.
Conclusion: Figure 1 Projected Total ICU and General Medicine Team Acute Care Demand