I have no charts today...too busy with actual work! I did look at the numbers, and they are mostly as expected. Colorado had a large increase in cases and deaths, but the note on the State Health Department website indicated that was due to the incorporation of older data that had not yet been recorded. This just points to the ongoing problem of data reliability.
I hope to be able to post more analysis tomorrow.
Friday, April 10, 2020
Thursday, April 9, 2020
COVID-19 April 09, 2020
I'll be showing mostly plots with linear axes today, because that format brings out a lot of nice details that I'd like to discuss.
First and foremost, I'd like to emphasize how much the curve has flattened for both the number of infections and for deaths. The first figure below shows the cumulative number of infections. For a long time, we were following a very steep exponential curve similar to the blue dotted line. The data has now departed significantly from that exponential function. The best-fit exponential function of all the data no longer does a good job, and that's a really good thing. Instead of hitting 1,000,000 total cases this week, as we would have had we stayed on that steep curve, we are at less than half that. The three-day curve fit is also below the 10-day, which is indicative of further flattening. I would caution, however, that some of the biased weekend data is still influencing these curve fits.
A similar story can be told in the plot of total deaths. We have departed significantly from the initial steep exponential growth. Whereas 100,000 deaths seemed to be coming within the next two weeks, the current trends suggest that grisly number is much farther off, if it will be attained at all. Doubling time of deaths is still around 4 days, which is still very high, but it's better than doubling every two or three days. Hopefully, the trend will continue.
The daily number of new infections has almost recovered from the very low spurious weekend reports. It will be interesting to see if today's numbers and Friday's numbers make up the difference. The offset in the daily rate is still obvious, and the rate is almost where it was before the weekend. Note that this plot is the only one with a semi-log axis, so it may be hard to see the details.
The daily death rate (on a linear axis plot) clearly shows the effect of the weekend numbers. There was a spurious drop followed by a slight over-correction the day before yesterday. Yesterday's numbers settled to a value almost exactly as expected. My guess is that today's numbers and Friday's reports will continue that trend followed by another weekend of bad data.
First and foremost, I'd like to emphasize how much the curve has flattened for both the number of infections and for deaths. The first figure below shows the cumulative number of infections. For a long time, we were following a very steep exponential curve similar to the blue dotted line. The data has now departed significantly from that exponential function. The best-fit exponential function of all the data no longer does a good job, and that's a really good thing. Instead of hitting 1,000,000 total cases this week, as we would have had we stayed on that steep curve, we are at less than half that. The three-day curve fit is also below the 10-day, which is indicative of further flattening. I would caution, however, that some of the biased weekend data is still influencing these curve fits.
A similar story can be told in the plot of total deaths. We have departed significantly from the initial steep exponential growth. Whereas 100,000 deaths seemed to be coming within the next two weeks, the current trends suggest that grisly number is much farther off, if it will be attained at all. Doubling time of deaths is still around 4 days, which is still very high, but it's better than doubling every two or three days. Hopefully, the trend will continue.
The daily number of new infections has almost recovered from the very low spurious weekend reports. It will be interesting to see if today's numbers and Friday's numbers make up the difference. The offset in the daily rate is still obvious, and the rate is almost where it was before the weekend. Note that this plot is the only one with a semi-log axis, so it may be hard to see the details.
The daily death rate (on a linear axis plot) clearly shows the effect of the weekend numbers. There was a spurious drop followed by a slight over-correction the day before yesterday. Yesterday's numbers settled to a value almost exactly as expected. My guess is that today's numbers and Friday's reports will continue that trend followed by another weekend of bad data.
Wednesday, April 8, 2020
COVID-19 April 08, 2020
With last weekend now in the rearview mirror, the systematic bias of weekend reporting becomes increasing clear. Let's start with the daily death rate. The numbers on Sunday and Monday had fallen compared to prior days. There was a lot of press about this. You can see this very clearly, because I've switched to a linear axis for these data. Then yesterday's numbers came in, and the press switched to reporting that we had the highest numbers of daily deaths yet recorded. In fact, you can see that yesterday's data falls very close to where it should be based on both the 10-day exponential trend and the Gompertz model. The real story, which is still being missed, is that Sunday's and Monday's numbers are bullshit.
Total deaths continue upward. The trend is continuing to flatten with the 10-day exponential and three-day exponential models below the long term exponential. Some of the flattening, however, is a result of the bias in the weekend numbers. I expect fairly large increases today through Friday as the backlog of both tests and deaths hits the books.
The total number of infections has also departed from the long term exponential fit; the curve is also flattening. I've plotted the total infections on a linear axis to make this more obvious. The daily rate of change of infections is still going upward. You can see the discontinuity and offset of the data in the last three days resulting from the biased weekend data.
Total deaths continue upward. The trend is continuing to flatten with the 10-day exponential and three-day exponential models below the long term exponential. Some of the flattening, however, is a result of the bias in the weekend numbers. I expect fairly large increases today through Friday as the backlog of both tests and deaths hits the books.
The total number of infections has also departed from the long term exponential fit; the curve is also flattening. I've plotted the total infections on a linear axis to make this more obvious. The daily rate of change of infections is still going upward. You can see the discontinuity and offset of the data in the last three days resulting from the biased weekend data.
Tuesday, April 7, 2020
COVID-19 April 07, 2020 Special Colorado Edition
With today's numbers hot off the press, the range of possible Gompertz model outcomes has narrowed. Baring some strange event, I feel reasonably confident with the Colorado predictions. What does "reasonably confident" mean? I think they are upper limits and the actual numbers will not be more than about 30% higher at most, probably lower. Maybe I'll eat some crow later. We'll see. Maybe I'll eat some crow later. We'll see.
So what do the numbers say? The Gompertz model (see previous posts about this model) predicts 20,000 total infections. The number of new daily cases will peak at 441 on April 11. Colorado will reach 10,000 cases--halfway to the final number--on April 18. Final deaths will be 800. The peak number of daily deaths will be 18 on April 15. Colorado will reach 400 deaths--halfway to the final number--on April 21.
What's interesting about these predictions is that the Gompertz growth rate for both infections and deaths is the same: 0.06. Yet, the curve fits for both data sets were arrived at independently. The fact that they have the same growth rate provides a good amount of confidence in the predictions. Assuming that deaths are proportional to the number of infections, you'd expect to see the growth rate be about the same. Furthermore, note that the peak in deaths and the halfway point for deaths lags the infection case milestones by about four days. This delay between the official infection report and death is reasonable. Thus, the two model results for infections and death are consistent.
COVID-19 April 06, 2020
Yesterday, I made a point of describing how screwed up the weekend data appears to be. Several of you chimed in with anecdotal information that was in concurrence. Thank you!
I thought I'd follow up with a little bit more analysis and data. I'll let you decide. Below is a plot of the number of new infections each day. The reported data is in blue. The orange data represents predicted numbers based on a Gompertz model. I've plotted this on a linear scale rather than the log scale I've typically been using. The linear scale lets you see variations easier than a log scale. See those last two points? I've circled them in red. Those are the data that were reported on Sunday and Monday. To my eye, the Sunday data is way, way out of family with every other data point up to that point. The Monday data is a little better in that it is at least increasing again. I've seen similar aberrations previously. I've circled those in green. The earlier times aren't as obvious as the ones this weekend, but that's because all the numbers were much smaller back then. But, the blips are there. There are similar patterns in many, but not all, of the 50 states. Anyone want to lay odds that we'll see the same pattern next weekend?
It will be interesting to see if we get a flood of data coming in later this week to make up the difference. It's possible (likely?) that agencies and labs are not working on the weekends or are at least running with minimal staff. Let's also remember that testing is still not able to keep up with demand even when labs are going full bore.
In the meantime, what I believe to be spurious data is affecting the trends. So, for now, those low numbers have slightly slowed the doubling rate. I've seen a lot of press and reports stating how good the numbers were this weekend. I would exercise caution. Those numbers could be real. Or not.
I thought I'd follow up with a little bit more analysis and data. I'll let you decide. Below is a plot of the number of new infections each day. The reported data is in blue. The orange data represents predicted numbers based on a Gompertz model. I've plotted this on a linear scale rather than the log scale I've typically been using. The linear scale lets you see variations easier than a log scale. See those last two points? I've circled them in red. Those are the data that were reported on Sunday and Monday. To my eye, the Sunday data is way, way out of family with every other data point up to that point. The Monday data is a little better in that it is at least increasing again. I've seen similar aberrations previously. I've circled those in green. The earlier times aren't as obvious as the ones this weekend, but that's because all the numbers were much smaller back then. But, the blips are there. There are similar patterns in many, but not all, of the 50 states. Anyone want to lay odds that we'll see the same pattern next weekend?
In the meantime, what I believe to be spurious data is affecting the trends. So, for now, those low numbers have slightly slowed the doubling rate. I've seen a lot of press and reports stating how good the numbers were this weekend. I would exercise caution. Those numbers could be real. Or not.
Monday, April 6, 2020
COVID-19 April 05, 2020
Are you an optimist or a pessimist? The optimist will take the view that yesterday's numbers are good. The number of new cases dropped dramatically, and we failed to reach 10,000 deaths due to a drop in the number of daily deaths. The pessimist will look at the numbers from yesterday and find them improbable. I'm an optimistic pessimist. I hope the numbers are real, but they look very suspicious. I saw a similar pattern in the data from last Sunday, and I suspect the low numbers are a result of numbers either not being officially tallied by the state health departments or the state health departments not reporting a complete tally. Last week, a spike in numbers came in on Monday and Tuesday after seemingly low numbers on Sunday. Let's see what happens this week.
Look at the Daily Rate of Change graph and the Daily Death Rate graph to see how different yesterday's numbers are from the historical trend.
Look at the Daily Rate of Change graph and the Daily Death Rate graph to see how different yesterday's numbers are from the historical trend.
Sunday, April 5, 2020
COVID-19 April 04, 2020
I'm going to make this short today because it's a beautiful spring day here in Colorado. I want to get outside, work in the garden, and go for a nice walk/run wearing a socially responsible mask.
The usual charts are below.
As a reminder, each day's data is valid for the end of the day before. So, today's report represents the final numbers from yesterday. Tomorrow will tell us how today ended, and so forth.
Yesterday's total cases for the U.S. came in at 307,876. The doubling time is currently 4.8 days and decadaling time is 16.0 days. Both of these times have generally been increasing in length very slow each day. That's a good trend, but it would be nice if it were faster. At the current rates, we will hit 1,000,000 total cases in a little over 10 days.
Total deaths came in at 8,360. At the current rate, we will hit 10,000 sometime today, or come very close. We'll see the reality of that in tomorrow's report. The doubling time is now 3.1 days and the decadaling time is 10.4 days. That would mean we will reach 100,000 deaths in less than two weeks from now if current trends continue.
As a reminder, each day's data is valid for the end of the day before. So, today's report represents the final numbers from yesterday. Tomorrow will tell us how today ended, and so forth.
Yesterday's total cases for the U.S. came in at 307,876. The doubling time is currently 4.8 days and decadaling time is 16.0 days. Both of these times have generally been increasing in length very slow each day. That's a good trend, but it would be nice if it were faster. At the current rates, we will hit 1,000,000 total cases in a little over 10 days.
Total deaths came in at 8,360. At the current rate, we will hit 10,000 sometime today, or come very close. We'll see the reality of that in tomorrow's report. The doubling time is now 3.1 days and the decadaling time is 10.4 days. That would mean we will reach 100,000 deaths in less than two weeks from now if current trends continue.
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