Hospital Resource Calculator for COVID-19

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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 http://covid19forecast.rush.edu/ 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.

Picture of forecast tool to select growth model and location.
Top of tool – select growth model and location

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%.

Selection for proportion of coronavirus patients visiting your hospital system.
Select the proportion of novel coronavirus positive patients visiting your hospital

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.

Selection for hospital admission parameters
Select the values to model hospital admissions

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.

Selection for personal protective equipment usage
Select the number of units of PPE used per day per patient

Adjusting Forecast Length

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

Selection for forecast length
Select the number of days for the forecast length

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.

Tool displays graph and table of confirmed novel coronavirus cases in state
Tool displays forecast of confirmed novel coronavirus cases in state and admissions to hospital

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

Graph and table of bed needs by type by day
Tool displays forecast of hospital bed needs by day

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

Graphs and tables of number of PPE type required per day
Tool displays forecast of required PPE per day

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 ~ ex) 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 (2nd order polynomial)

In other locations, a 2nd order polynomial (y ~ x2 + 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

COVID-19 Continues Rapid Spread Through US

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Over the past week, a tremendous amount has changed in the world. Governments, employers, and social networks have advocated social distancing through travel bans, closures of schools, working from home, and countless other cancelled activities. The goal of these activities is to slow the spread of COVID-19 and protect vulnerable populations.

In our post that we released one week ago, data suggested the growth of COVID-19 was consistent, yet slower in the United States than in Europe. Continuing to use data from Johns Hopkins University Center for System Science and Engineering, we are now seeing that transmission rate change.

Updated Comparison of Growth

Since March 1st, 2020, the rate of transmission in the United States matches that of several of the major European countries. In Figure 1, we see the growth of COVID-19 cases grow at similar rates to Italy, France, Germany, and the United Kingdom.

Figure 1.

Confirmed cases of COVID-19 since March 1, 2020 for US and Four Major European Countries

China and South Korea had fast transmission growth months ago, but enacted strict social distancing policies. In Figure 2, we see the growth of COVID-19 cases in these countries has almost stopped, unlike in the US.  At these current rates, the number of confirmed cases in the United States will pass South Korea in less than a week.

Figure 2.

Confirmed cases of COVID-19 since March 1, 2020 for US, China and South Korea

An estimated growth factor for each country was calculated from the confirmed cases data. Of these seven countries displayed in Table 1, the transmission growth rate is the fastest in the United States, but not different from France, Germany, and the United Kingdom. Italy, South Korea, and China are statistically slower.

Table 1.

Table of the growth factor estimated and implied days to double for a number of countries, including the US

Forecasting Future US Cases

Using the data for confirmed cases in the United States since March 1, we created a forecast for the COVID-19 spread in the US over the next two weeks. The interactive forecast displayed in Figure 3 assumes the transmission growth rate of the last 14 days will continue over the next two weeks.

Figure 3.

From this forecast, we believe rapid growth of new cases will develop during the last week of the month. Our model also suggests that United States may approach half a million cases by the end of March. Whether this estimate is accurate or an overestimate is dependent on our ability to test patients and society’s willingness to comply with mitigation efforts.

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

Comparison of COVID-19 Growth Rates

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The global coronavirus (COVID-19) outbreak has elicited widely varying responses by national governments and societies. In evaluating opportunities for mitigating the spread of COVID-19, Anderson, Heesterbeek, Klinkenberg, and Hollingsworth (2020) identified personal and governmental responsibilities toward slowing the transmission of the virus. Identifying successful strategies from transmission data is critical toward preventing further catastrophic outcomes.

Over the last several months of intensive surveillance, Johns Hopkins University’s Center for System Science and Engineering  (JHU CSSE) has provided a public data set curated from a number of international data sources, including the WHO, China CDC, and the US CDC. In addition to their online dashboard, the Center has published the data publicly on GitHub. This data has allowed for widespread education and investigation into COVID-19 activity.

For institutional preparedness plans, knowing the volume of cases over time is a critical factor in understanding staffing and equipment needs.  In addition, to have a framework to examine if local transmission rates are growing above or below expectations can help to understand timelines for surge capacity needs.  We used recent epidemic growth rate data to develop a predictive model for COVID-19 case counts.

COVID-19 Spread

As of March 7th, 2020, 105,836 people across 101+ countries have been confirmed as infected by COVID-19 (JHU CSSE, 2020). Unfortunately, this has already resulted in 3,558 deaths internationally and 17 in the United States. Further insights from the confirmed cases data can help identify countries where the spread of COVID-19 has been slowed. These countries’ responses to mitigating spread can serve as best practices.

Using the JHU CSSE data set of confirmed cases, we aggregated the daily case count at the national level. The cases count from each nation was aligned making time zero (t=0) the day with the first reported case. Only seven of the 101 countries started with confirmed cases on the first day of data reporting, and only Mainland China (547), Thailand (2), and Japan (2) had more than one case. While Mainland China will be included in the remainder of analysis, little is known about the early spread of the virus.

Next, utilizing principles from the physical sciences, the case counts were log transformed to better investigate the transmission growth factors. In Figure 1, we observed the log transformed rates of confirmed COVID-19 cases from the first infection for the five countries with the most cases and the United States (currently 9th). Mainland China, South Korea, Italy, and Iran all show strong signs of diminishing growth (bending of the curve), which in not yet seen in France or the US. Another interesting observation is a lag in explosive growth from the initial infections, which could be interpreted as the time before community spread of the virus. In Italy, the lag was around 20 days from the first confirmed case. In South Korea, France, and the US, the lag was approximately 28-32 days.

Figure 1. Confirmed Cases by Days Since First Case

Shows the growth of COVID-19 by select countries after the first case

Qualitatively, the observed epidemic curves appear to have two different phases.  In most countries, an initial phase in which cases were likely imported to local communities and testing was limited, is followed by a second phase characterized by community transmission. Of most interest is the comparison of rates of community transmission in this second phase because this may identify countries with the slowest rates of transmission, and may suggest the most efficient infection control strategies.

Assessing Community Spread Rates

To assess the growth of cases with community spread, each country’s data was aligned to time zero (t=0) identified by the last point of the lag period. Data was re-aligned for the 17 countries and regions with over 100 confirmed cases. Figure 2 displays the log transformed re-aligned confirmed cases curves for these countries. The curve for the United States was designed with each data point identified for ease of identification in the graph.

Figure 2. Confirmed Cases by Days Since Estimated Community Spread Start

Shows the growth of COVID-19 by country after the estimated start of community spread

The most important feature of the curves in Figure 2 is the slope of the curve, as this is an indicator of transmission growth rates. The curves for Mainland China, South Korea, Singapore, and Hong Kong show signs of diminishing growth meaning the rate of further infections is declining. Many of the other curves, including the United States, are more linear meaning that the infection rate has not started to slow. This data also shows differing slopes meaning the infection rate in the various countries is different. Some are experiencing faster spread and some have slower spread.

Ranking the COVID-19 growth by Country/Region

The rate of growth of COVID-19 in countries can be compared by estimating the transmission growth factor from the series of daily confirmed case count. The transmission growth factor indicates how fast COVID-19 will spread; larger numbers imply faster growth. Using linear approximation for the slope of the curve, we identify a wide range of transmission growth factors in each country, which are shown in Table 1. Additionally identified in the table are the implied days for the cases to double, days to go from the 1st to 100th case, and days to go from the 100th to the 1,000th case. As the growth factor increases, the measure of days decrease.

Of these identified countries, Belgium has the most aggressive growth factor followed by The Netherlands, Norway, and Iran. The United States has one of the slower growth rates, but is higher than the current rate in Japan, Mainland China, Singapore, and Hong Kong. It is worth reminding that a limitation of this data set is that the initial spread of COVID-19 in China is undocumented in the data set. However, the rate of continued spread in China is less than in the US.

Table 1. Growth Factor Estimate and Implied Growth Periods for COVID-19 Spread by Country

Table that compares rates of COVID-19 spread by country, includes calculation on days to number of 
infections

Conclusion

This analysis has relied on preliminary data of COVID-19 global confirmed cases to determine the rate of spread in various countries. In the United States, COVID-19 is currently spreading slower than in many other highly impacted countries, but this should not be a signal of complacency. The daily data is currently showing a consistent rate of growth, not a declining rate. Because we are still in the early days of this infection, it is imperative to continue domestic mitigation efforts to slow or stop the continued spread of this deadly virus.

Promising future research could continue to look at the form of the COVID-19 transmission rates as this epidemic continues to evolve. Additionally, more information and evaluation on the specific interventions employed by varying countries could help build best practices for the current situation and future episodes.

Written by Thomas A. Webb, MBA, and Bala Hota, MD, MPH

References:

Anderson, R. M., Heesterbeek, H., Klinkenberg, D., & Hollingsworth, T. D., (2020). How will country-based mitigation measures influence the course of the COVID-19 epidemic? The Lancet. Retrieved from https://www.thelancet.com/pb-assets/Lancet/pdfs/S0140673620305675.pdf

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