The COVID-19 response team at Ohio State and the Infectious Diseases Institute has been charged with predicting outbreak size and hospital burden with COVID-19 throughout the state. These predictions are supplied to the Ohio Department of Health and the Ohio Hospital Association to be considered in their decision-making process. The public is understandably interested in these model predictions. We describe in this blog post a bit about our model, and in particular how recent trends in the data have resulted in revised, lower predictions from our model on outbreak size. For the interested reader, technical description of our methods can be found here.
Exponential growth, diverted
Let’s start with some data.
Here is a plot of lab-confirmed COVID-19 cases in Ohio through the month of March. Up until March 17, on a log-scale, the counts of new cases each day are fit very well by a line with positive slope. This corresponds to exponential growth — a very rapid increase in cases over time. Our initial model predictions based on these data anticipated a surge of cases in mid-April, enough to severely strain Ohio’s healthcare system.
Then, beginning on March 17, the case data take an abrupt turn: case counts suddenly level off. Rather than growing exponentially, we see approximately a constant number of new cases per day1. In the case count plot, there is a break at the dashed line, and suddenly the slope of the line changes.
This dramatic flattening of the case curve is reflected in our revised predictions, which are much lower than our earlier ones. We understand that this change in model output may be unsettling2 — but the sudden change in course of the data is the reason.
Models learning from data
This brings us to an important point: our model has parameters (numerical characteristics) and these parameters are estimated from the data. As we “feed” the model new data, the parameter estimates are revised and updated, and so are the corresponding model predictions. In this sense, we say that the model “learns” from the data.
This feature of continuously updating the model based on incoming data is shared by many models even when they are very different in their structure. For example, the IHME COVID-19 model also learns from the data. The approach of the IHME model is completely different than ours — it takes a purely statistical approach that models the cumulative number of deaths over time, while we model a dynamic epidemic process on a network, calibrated on onset times of lab-confirmed cases. But IHME similarly has drastically reduced their predicted hospitalizations and COVID-19 deaths from earlier estimates. This reflects that both our model and the IHME model are seeing an abrupt slowing of the epidemic in the data.
Indeed, our predictions as of April 6 may still be over-estimates, as these predictions give weight both to the early exponential growth portion of the data (before March 17) as well as the flattened portion of the curve (after March 17). As more data accumulates, the pre-March 17 data will comprise a smaller portion of the data, and the post-March 17 data will dominate. If the flattened curve persists, our model predictions on hospital demand may further decrease.
Social distancing matters
The sudden change in the case curve from exponential to near-linear growth is not typical of epidemics — a smoother, more gradual change is usually observed.
Of course, the state’s response to COVID-19 has not been typical, either. A brief timeline of social distancing measures that have been implemented in Ohio is given below:
- March 5 — spectators prohibited from Arnold Sports Festival
- March 9 — Ohio declares a state of emergency
- March 12 — large gatherings prohibited
- March 15 — bars and restaurants closed
- March 17 — polls closed as a health emergency
- March 17 — statewide school closures3
- March 18 — barbershops, beauty salons, tattoo parlors closed
- March 23 — Ohio Department of Health issues stay at home order4
The response of the Ohio Department of Health and Governor DeWine was swift. Notice that many of the social distancing orders took place prior to the change point in the case curve, potentially in time to drive the change. The stay at home order may also be significant in pulling down the latter portion of the curve, and its effects may become more apparent as more data become available5.
Empirical data (data collected through observation and experimentation) indicate that social distancing measures have had substantial impact on behavior. For example, cell phone data show marked reductions in movement across Ohio and in other states. Syndromic surveillance data show a spike in sales of thermometers and over the counter cold and flu medicine in mid-March6. Anecdotally, there was a spike in toilet paper sales as well, as anyone who tried to go shopping at that time can attest. Usually it’s not difficult to find Charmin; people’s behavior clearly changed.
Our model cannot distinguish between correlation and causation regarding social distancing and the abrupt change in the case curve. The simplest explanation, however, is that changes in behavior driven by social distancing measures have shifted the epidemic from a rapidly growing one with the potential to overwhelm the healthcare system, to a much gentler curve that may be close to or already at its peak.
Of course, this gentler path is not set in stone. If it is driven by social distancing, relaxing distancing measures has the potential to put us back on the path of a large epidemic. When and how to open the state is a difficult question, and ultimately a policy decision. We are not policy makers — we are a team of scientists, and will continue to offer our best scientific judgement on COVID-19 dynamics based upon the data available.
1After March 17, the slope of the curve is close to zero. It might be slightly positive or slightly negative, but it is small in magnitude. This has been noted by other observers as well. For example, Nate Silver in an April 9 tweet regarding U.S. COVID-19 data: “Things have flattened out quite a bit. It’s hard to tell whether they’ve flattened but still sloping up, flattened but now sloping down, or what…”.
2“We cannot make head or tails of the model…Please consider COMPLETELY re-doing these models” — Representative email sent to us on April 9, capitalized as in the original. We appreciate the lack of cursing.
3The governor’s order closed schools at the end of Monday, March 16 for three weeks. Some school systems closed earlier — for example, Columbus City Schools closed at the end of the day Friday, March 13. The school closure order was subsequently extended to May 1.
4The stay at home order was subsequently extended to May 1.
5Due to wait times of getting test results and between test date and illness onset, our data on reliable counts of case onsets lags several days behind the current date.
6Ohio Department of Health Syndromic Surveillance COVID-19 Summary: Monday, April 6, 2020.