Epidemic Curves, Part Deux

Dave continues to explore the shape of epidemic waves and whether they are predictable in some manner. And we keep thinking about why a wave would have the shape it does–what is the math telling us about the underlying reality. Dave’s notes:

As part of our examination of the some of the basic mathematical properties of covid case surges, we recently modelled the surges as a simple parabola here: https://healthy-skeptic.com/2022/02/10/case-wave-trajectory/ Since the parabola models the main portion of the surge pretty well we decided to see if it was possible to use a parabolic curve fit to predict the trajectory of a surge in real time.
In the attached animation we display the results of calculating a series of parabolic curve fits to the Omicron surge in Minnesota, starting with 3 days of case data, and adding one more data point each day highlighted in solid green, while the complete actual cases curve is in light grey. We used 7 day running average cases per day, so the surge is modelled to start on 12/27/2021, a week after the cases started to rise on a daily basis. The first curve fit, for 12/29/2021, therefore has the case data for 12/27, 12/28, and 12/29. For these 3 days the cases per day were actually still accelerating higher, and so the parabolic curve fit ramps up higher as well. Each day after that we add one more days’ data and calculate a new curve fit (which as a green dashed line). Even until 1/08/2022, close to the actual peak, cases were still accelerating higher and the predicted parabolic curve fit was still accelerating as well. Only around 1/17/2022, when we were actually about one week past the peak, did the resulting curve fit start to look somewhat close to the actual trajectory of the average cases.
It is clear from this exercise that a simple curve using actual daily data will not be likely to be able to successfully predict when the peak in cases in occur. An additional problem is that we used completely reported actual cases for this analysis. If, however, we had been doing this in real time as Omicron was going higher, the daily cases would have been incompletely reported for 1 to 2 weeks after the specimen collection date. For this reason, even if this technique successfully predicted the peak in cases, the reporting lag would still prevent us from predicting the peak before it occurred.
There are other types of curve fits used to model epidemiological case waves, and we may pursue those in the future. We may, for example, attempt to model the case wave as normal distribution, or bell curve, and us the initial slow ramp up as the predictor for the overall height of the wave. Regardless though of what model is used the basic problem of case reporting lags will limit the ability to accurately predict the shape of the overall wave in real time.