This page will be updated in the next few days, after a One-month hiatus.
Until Then, Follow the Link Above for Updates.
COVID-19 Doubling-Time Model and Projections
BY DAN REICHART, NICK KONZ, AND ADAM TROTTER
Updated 5/4/20209
The point of this page is to model the COVID-19 doubling time. This is the time that it takes for twice as many people to become infected with the virus. In early March, the doubling time was approximately 2 days in the United States. At this doubling rate, it would have taken only 40 days for nearly everyone in the United States to become infected.
As such, we began to take measures to increase the doubling time. The most effective way to do this is through widespread testing, which allows cases to be identified, identified early, and isolated. Unfortunately, widespread testing of the symptomatic was slow-coming in the United States, not beginning in earnest until mid-March. And widespread testing of the asymptomatic (see below) hasn’t begun yet.
Without both of these, we have instead had to rely on significant lifestyle changes: social distancing, frequent hand washing, mask wearing, etc. However, these lifestyle changes must be adopted by nearly everyone, and adhered to vigilantly, to be effective.
We can see if these efforts are working in the United States, and how well they are working, by monitoring the doubling time.
The low, open circles are excluded from the fit because testing was ramping up in the United States during this period, resulting in fewer cases being missed than even the day before. This was of course good news, but it also meant that artificially low doubling times were measured during these days (dashed curve). These measurements also meet Chauvenet’s criterion for being outlying, and consequently are rejectable on purely statistical grounds as well.
Using data from here, we have calculated each day’s doubling time based on each day’s new cases. These are plotted to the left, and we will try to update this plot (and the other plots and numbers on this page) daily. The good news is that the doubling time is increasing — although no longer at an accelerating rate.
So far, the data demand nothing more sophisticated than a “smoothly broken” linear model. We fit this model to the data using our TRK statistic, which accounts for not only the plotted error bars, but also for the additional scatter that is clearly present. In short, this ensures that we do not underestimate the uncertainties in the following values. (For the technically minded: We model this scatter as log-normal, so smaller for shorter doubling times and larger for longer doubling times).
On any given date, there is a 68.3% chance that the true doubling time lies between the green curve (our optimistic scenario) and the red curve (our pessimistic scenario). We find that as of yesterday, the doubling time was
28.5 +/- 0.9 days
and that it is increasing by
18.7 +/- 1.0 hours each day.
Since the doubling time is increasing by about one day each day, this means that we are near or slightly past the peak.
These projections are similar to what the professionals are finding under different mitigation scenarios. Our projection model is simpler, but has the advantage of assuming nothing. Rather, we are simply extrapolating current changes in behavior, as reflected in the daily doubling-time measurements.
The next question is if this rate of increase in the doubling time is enough to squash the post-peak tail. In the plot to the right, we calculate the number of new reported cases that we should expect each day, assuming that the doubling time continues to follow the blue (baseline), green (optimistic), and red (pessimistic) curves above.
Note that “reported cases” is not the same as “infections”. This is because it is now known that 50% — 75% of infections are asymptomatic. Consequently, in countries like the United States where there are only enough kits to test the symptomatic, most carriers of the infection are missed. The effect of this is twofold: (1) more infections (and more cases) early on, and an earlier peak, but (2) fewer infections/cases overall, because you establish a greater degree of herd immunity. We include this effect in our projections: In our baseline scenario (blue curve), we assume that 2/3 of carriers are being missed. In our optimistic scenario (overall, green curve), we assume that 3/4 are being missed; and in our pessimistic scenario (overall, red curve), we assume that only 1/2 are being missed.
These projections also depend on how long the infected stay infectious. This depends on many things, including how early carriers are identified and isolated. In our optimistic scenario, we assume a short, half-week infectious period. In our baseline scenario, 1 week. And in our pessimistic scenario, 2 weeks. (However, this is a minor effect, especially now that we are post-peak.)
The Peak: Overall, we projected a peak of approximately
94 thousand new infections per day
corresponding to
31 +/- 2 thousand new reported cases per day
on
April 18th.
The sudden drop corresponds to when the testing ramp-up phase leveled off in late March, which allowed new data to begin to inform our model again.
The plot on the left tracks how our projected peak number of new reported cases per day changed with time. As the doubling time increased faster, these numbers fell accordingly.
The uncertainty increased in late March, when we learned of the large, asymptomatic population of carriers.
The plot on the right tracks how our projection for when this peak would occur changed with time.
The Tail: How many people will be infected, and how many people will die, if we cannot increase the doubling time faster than we currently are?
The total number of reported cases at any date is given by summing our projection curves above, which we do in the plot to the left.
Overall, we project that approximately
7.7%
of Americans will become infected prior to September 1, 2021 (our current best guess as to when a vaccine will be readily available). This corresponds to approximately
2.6% (+0.9%, -0.6%)
of Americans becoming symptomatic and identified.
However, this does not mean that this many people will become infected. Again, if we can increase the doubling time faster than we currently are, and if we can do this sooner rather than later, only a very small fraction of the population need become infected.
Deaths: We calculate the fraction of reported cases that will result in death by dividing the current total number of deaths by the total number of reported cases from 6 +/- 1 days ago — this is a best guess as to the lag between a case being reported in the United States and death occurring, for cases that result in death. Given this, we currently find that
6.8% +/- 0.2%
of reported cases in the United States result in death. If this percentage holds, this would correspond to
570 (+210, -140) thousand deaths.
Again, this happens only if we do not increase the doubling time faster than we currently are.
The sudden drop corresponds to when the testing ramp-up phase leveled off in late March, which allowed new data to begin to inform our model again.
In the plot to the right, we are tracking our projected total number of deaths, converting from total reported cases to total deaths using the reported totals available on that date.
Final note: These numbers are scary, but they are not intended to scare. Actually, they are meant to be empowering. We have the power to change these projections by taking this crisis seriously and altering our lifestyle for the weeks and months ahead.
It would also be very helpful if the federal government could make more testing kits available, and quickly. This has had a significant impact in countries like South Korea.