We develop an analytical tool using computer simulation techniques to address hospital pandemic planning problems. In the following, we calibrate the simulation inputs based on carefully researching the clinical evidence, and develop a DES model of the patient flow in the COVID unit. Finally, we use real world data to validate the simulation model.
Input analysis
The daily COVID hospitalizations are not time-homogeneous and cannot be modeled as a simple Poisson process. For planning purposes, the future patient arrival is obtained from a data-driven SEIR model. The traditional SEIR model describes a stochastic process with four states, representing the susceptible, exposed, infectious and recovered population, denoted as and . The challenges reside in calibrating the control parameters that govern the system dynamics, e.g., how fast the exposed population migrates to the infectious population. In this study, we use historical data [13] to train the model parameters and dynamically adjust the basic reproduction number, , the factor that dictates the doubling time of infectious cases. Before any interventions, we numerically get the optimal and optimal (the day of the first community-spread case) by minimizing the mean squared error of the reported infectious-population and the infectious-population generated by our SEIR model. To detect the change of with stay-at-home orders in place, we conduct curve-fitting using the time series estimate of of several European countries including Italy, Spain and Germany. These countries have implemented the order early enough to provide sufficient observations for model calibration. After the lockdown order is released, will change gradually according to the fitted time series curve. In this way, we are able to predict the disease spread down to the county level and will help individual hospitals to understand the future demand given regional-specific situations.
The range of epidemiologic variables, e.g., hospitalization rate, hospitalizations that require ICU stay, denoted as ICU rate, hospital length of stay by unit type (ICU vs ward), and case fatality rate are determined by review of the literature and expert consensus of the team. We provide a table (Table 1) below to summarize the basic setting. The total number of existing beds, and potential surge beds for use in ward and ICU are provided by the hospital. Currently, 35 beds are reserved for the COVID unit of UF Health Jacksonville.
Model conceptualization
A DES model based on the general patient flow in hospital COVID units is developed using a commercial simulation software Arena®. Patients arriving at the hospital will be triaged first. Mild patients will be directly discharged after administering the treatment. Severe patients, based on their level of severity will be admitted to ICU (critical condition) or ward (non-critical, e.g., do not need ventilators). Due to the dynamic progression of diseases, patients’ condition can elevate and they need to be admitted to ICU from ward. Patients in ICU experience the critical condition (stage 1) and then are stabilized (stage 2). ICU patients can be stepped down to ward when necessary (e.g., to make room for a critical condition patient). If not treated promptly, patients developing severe complications will die (see Figure 1).
Model validation
The validity of the model was tested against different assumptions, and the historical census data were used to compare with the model outputs. In particular, we focused on the catchment area of UF Health Jacksonville. It is a metropolitan area with 1.5 million people, covering five counties: Baker, Clay, Duval, Nassau, and St. Johns, Florida. Daily confirmed COVID cases in these counties were obtained from the Florida Department of Health (FDOH) website [17]. The historical case data were used as the patient arrival input to replace the SEIR model prediction for validation purposes. The real hospital patient census in the COVID unit (ward and ICU) were provided by UF Health Jacksonville. The bed capacity was set as 10 for the ICU and 25 for general wards. Other parameters were the same as those in Table 1.
Sensitivity analysis
We constructed several scenarios each intended to highlight some particular aspect of the disease profile characteristics (Table 2) and investigated the resulting supply implications. In particular, we varied the range of market size from 5%, 10%, and 15%, representing different patient diversions to the hospital. The hospitalization rates were set as 15%, 20%, and 25%; the ICU rates among the hospitalized patients were set as 15%, 25%, and 40%, representing different levels of severity of the disease. This yields a total of 27 scenarios. The bed capacity was set as 10 for the ICU and 25 for general wards. The patient arrival was simulated based on the SEIR model’s prediction of 100 days’ infected cases (March 18th to August 1st) of the metro Jacksonville area.