In a previous post, we provided estimates of confirmed cases for novel coronavirus across the United States. We believe the trends in cases have real relevance for individual health systems.

One question we have asked is, at what point will we begin to see rapid increases in the numbers of cases coming to our hospital? Currently, the number of cases presenting to any one health systems and any state is variable. There is rapid growth along the east and west coast. However, cases are beginning to accumulate in other parts of the country.

As local cases begin to rise, health systems need to prepare for intense resource utilization to safely and effectively treat patients infected with the virus. By using the successive confirmed case counts from Johns Hopkins University Center for System Science and Engineering’s github repository, we designed a web based tool that helps hospitals plan for forecasted resource use.

**The calculator can be found at https://rush-covid19.herokuapp.com/ or click here.**

### How to Use the Calculator

The goal of this calculator is to allow a hospital to understand its resource use, such as beds, ICU beds, ventilators, and personal protective equipment (PPE).

The top section of the tool is used to adjust the parameters.

#### Adjusting Growth and Admission Parameters

If Hospital A wants to forecast its future use of these resources, it would need to enter some baseline information. At the top of the page, select a model type (Exponential, Polynomial, or Logistic), and choose the state in which Hospital A is located. Please review the explanation of the growth models options further below or click here.

Below this, enter the % share of statewide COVID-19 cases that have come to Hospital A. For example, if the statewide count is 200, and Hospital A has seen 20, its rate is 10%.

Of these cases, the other parameters to enter are: the % of COVID-19+ patients seen at the Hospital that are admitted to inpatient, the % of admissions that require ICU care, and the % of ICU admissions that require mechanical ventilation. The average length of stay (LOS) for non-critical care and critical care for COVID-19 patients is also needed to calculate the number of beds required. Click here for a note on LOS modeling.

#### Adjusting Personal Protective Equipment Parameters

To estimate PPE utilization, the number of ** units of PPE used per day per patient** are listed. This is a product of the number of provider interactions for each patient, and the number of PPE items used by the provider each day.

#### Adjusting Forecast Length

A last item is a setting for the forecast length, or how many days in the future the model will display.

This calculator is effective for calculating the number of net new COVID-19 patients seen by a system each day, and how many of these patients will be in a hospital census over time. It also can help to forecast the demand for PPE over time based on patient volume.

As with any modeling, this has limitations. The model is most effective for a 7 day window, and the uncertainty for the prediction increases the further the forecast is projected. In areas with recent statewide initiatives like shelter at home, the model will not factor those initiatives in, though any such programs won’t show an impact for a 5-10 day time window.

### Resource Requirements Graphs and Tables

After parameters, the first graph and table displays the forecast for cumulative confirmed novel coronavirus case by day, the new cases by day, the number projected to touch the health system and the new admissions.

The next graph and table displays the daily bed needs by bed type (non-ICU and ICU) along with the project number of vents.

Finally, the last graph and table project the number of PPE required per day to safely treat the novel coronavirus positive patients.

### Notes on Modeling Parameters

To begin capturing the various phases of COVID-19 spread, we are constantly tracking the predictive success of three simple growth models (i.e., exponential, logistic, quadratic). These popular models have long been used to predict how populations, diseases, etc. grow, but can differ greatly in their predictions.

We are currently looking to strengthen our suite of models beyond these three general but often accurate examples.

#### Exponential Growth

The exponential model has been widely successful in capturing the increase in COVID-19 cases during the most rapid and difficult-to-mitigate phases. The exponential model takes a simple form (y ~ e^{x}) and essentially captures what happens when you repeatedly double a something over time (1, 2, 4, 8, …). As a model of uncontrolled growth, the exponential model has been one of the most accurate models at predicting the emergence of new COVID-19 cases across geographic scales within the US and abroad, from city to state, and country.

To date, in Illinois, the exponential model has most closely fits our data. Our hope is that the mitigation interventions that were implemented late last week will begin to favorably impact our case counts in the near future, but in the meantime we are preparing for the forecast volumes under this model.

#### Quadratic Growth (2^{nd} order polynomial)

In other locations, a 2^{nd} order polynomial (y ~ x^{2} + x) best fits the data and more accurately predicts the number of cases expected over the coming days. This kind of growth is typically described as quadratic and is the expected outcome when the growth rate changes and when that rate of change is constant. The rate of increase in this model is initially ** faster** than that of the exponential model. However, as time ensues and as the increasing growth rate stabilizes, the exponential model will produce faster growth.

Because of the inherent variability in COVID-19 data due to testing, reporting, and actual spread, it can be both difficult or easy to tell whether COVID-19 is spreading exponentially or quadratically. They key, is to not limit oneself to one model and to prepare for alternative outcomes.

#### Logistic Growth

As recovery ensues and as social planning begins to take effect, the rate of spread will eventually slow. At that point, the exponential and quadratic models will begin to fail, as we have seen for other diseases, epidemics, pandemics, and as we have seen for China and its cities and provinces in regards to COVID-19.

When exponential growth slows and then tapers off, it often becomes logistic, that is, the curve becomes “S” shaped. As we have seen with regions in China, the logistic model can accurately explain more than 99.9% of variation in the exponential growth and the tapering off.

However, the most powerful use and accurate predictions of the logistic model will require information on what the likely maximum number of cases will likely be under a combination of seasonality, spreading immunity, and active public health measures.

#### Length of Stay

Average LOS is a commonly used metric among hospitals. We modeled the expected change in size of a hospital’s COVID-19 patient population (ICU, Non-ICU, ICU on ventilator) using a common probability distribution, the binomial. If you’ve ever tried to predict the outcome of flipping coins, then you have intuitively used the binomial distribution where each outcome has a probability (p) of 0.5.

In short, we can use this distribution and average LOS to model what percent of 1-Day, 2-Day, … 10-Day, etc. patients will be going home or leaving on the current day. In doing this, we begin to account for daily carry-over and changes in the sizes of a hospital’s COVID-19 population.

More specifically, we use the cumulative distribution function of the binomial distribution with p = 0.5 (a patient goes home or they do not).

Click here to return to Adjusting Parameters

### Limitations

The model does not include PUIs that are admitted and subsequently test negative. At our center, these non-COVID-19 PUI patients are tested with results within 24-48 hours, and we factor those in as we use the output of the calculator. As we move further from the flu season, it is anticipated that a smaller proportion of PUIs will be non COVID cases.

### Authors

Kenneth J Locey, PhD, Jawad Khan, Thomas A. Webb, and Bala Hota, MD, MPH

### References

Johns Hopkins University Center for Systems Science and Engineering. (2020). *Novel coronavirus (COVID-19) cases* [Data file]. Retrieved from https://github.com/CSSEGISandData/COVID-19