COVID-19 April 20, 2020

The usual weekend data aberration was in full effect this weekend.  Both new daily cases and daily deaths took a dip.  The daily deaths, in particular, are starting to show a very, very large oscillation around the mean.  Over the last five days, there was a low yesterday of 1631 and a high of 2438 on April 15.  It was 1462 just two days prior to that.  So, there's an oscillation of about +/- 500 around a mean of about 2000, or 25%. That's huge, and it makes it very hard to pin down a curve that best fits the data. The variations in new daily cases are also similar, ranging from the mid-20,000s to the mid-30,000s.

Due to the very large oscillations, I will only be adjusting the best-fit curves roughly weekly.  If I try to adjust them daily, I will end up chasing the oscillating data up and down. For now, the curves fitting the cumulative statistics for total cases and total deaths are reasonably close to the historical data.

Some states, like Florida, are starting to reduce restrictions on social isolation.  It will be interesting to see how this affects the data.  At present New York and New Jersey still account for something like 40% of the numbers across the US.  These two states disproportionately affect the statistics, and the trend from those two stats has been overwhelmingly downward.  If states like Florida began to see an increase in cases and deaths, they could start to bend the curve back upward.  If that happens, it will invalidate the use of a Gompertz model, which assumes a relatively uniform infection process across the population.

It may very well be that to model the US it is necessary to model each state individually and then add the results together to obtain the solution for the country as a whole.  This is far too time consuming for me to undertake, but even if I was able the uncertainty in the models would likely increase beyond utility.  The certainty of statistical calculations often strongly depends on the number of data in the calculation.  As I already showed, the oscillations in the data aggregated across the US are already so large that the curve fitting is becoming problematic.  These oscillations are often worse at the state level and the number of data in each state is much smaller than the country as a whole.

COVID-19 April 17, 2020

Keepin' it short and sweet today.  Data from yesterday is plotted in the figures below.  I'm using only a linear scale today.  The Gompertz model continues to do a good job of representing the data.  The ups and downs of new cases and daily deaths continue their fairly repeatable pattern.  Yesterday was an up day.  I will likely not provide a report over the weekend unless something unexpected appears.  I do expect the weekend numbers to fall, followed by a rebound next week. 

COVID-19 April 16, 2020

Good morning from snowy Colorado.  Another fresh foot on the ground.  Normally, it would have likely been a snow day for the schools.

The adjustments I made to the model curves yesterday seem to be consistent with the data that came in yesterday.  Today, I made an additional very small adjustment that shifted things inconsequentially.  The curve fit is now very good.  Excellent, actually.  In the figure below, I have plotted the Predicted number of cases from the Gompertz curve vs. the actual number observed.  It's a beautiful straight line with a slope of 1.01, which is to say that the predictions are off, on average, by about 1%.  A perfect model would have a slope of 1.0.  The correlation is actually much higher: 99.99%.

The rest of the standard plots are shown below with a mix of linear and log axes.  I will call your attention to the daily case numbers and daily death numbers. The weekly oscillations have grown rather larger with a minimum around the weekend and a maximum around mid-week.  This makes curve fitting a challenge because rather than trying to get the model to reproduce the data, the goal is shifted to trying to match the average of the data.  As you can see, the model more or less goes right down the middle. The weekend data is too low, but yesterday's data pops up above the model.  There's little doubt that yesterday's data includes backlogged data from over the weekend.  I expect today's data to be a bit above the model, and then I expect things will start to fall again over the weekend.

COVID-19 April 15, 2020

The US numbers continue to be problematic from the standpoint of statistical analysis.  The expected weekend dip and subsequent rebound appeared, as predicted.  The magnitude of both the dip and rebound varies from week to week, and the varying data makes it difficult to determine the best-fit curve.

In the first panel below, the number of new daily cases, plotted on a linear axis shows the weekend alterations. The weekend before last there was a large, single-day drop followed by four days of upward growth.  This last weekend, there was a more continuous drop followed by a smaller rebound yesterday.

If I try to fit a curve to all the daily new case data (the blue dots), I find that there is no good solution.  In particular, the early data has a different behavior than the latter data.  This is seen most clearly in the second figure, which has the data plotted on a log scale.  The data in the shaded box has a different trend than the latter data.  I have decided to exclude these data from the curve fit and use only the latter data.  When I do that, I find the Gompertz curve shown by the red crosses.  Using this new fit generates different estimates of peaks and total cases than previously speculated.  The peak is now estimated at 32,300 cases, which already happened on April 7.  The analysis suggests we are on the downward slope.  Note that the data actually exceeded this estimate on several occasions, which is the nature of noisy data compared to a smooth statistical curve.

A similar issue was found when looking at the total, cumulative number of cases as shown in the next two figures.  Again, the early data shown in the shaded box has a different trend than the latter data. This should not be surprising since the it is the sum of daily cases that comprises the cumulative total.  Since the daily data has this behavior the cumulative sum shows it as well.  With the new curve fit, the total number of infections has been cut nearly in half compared to the previous estimate: 1.1 million.  On April 12, the halfway point of 550,000 infections was reached.

The cumulative deaths and daily death rate curves underwent a smaller adjustment.  Note, however, that the data has similar weekend noise problems, as specifically noted on the daily death rate chart.  The total projected deaths at this point is 120,000.  The halfway point of 60,000 is still ahead of us on April 29.  This is tragic, but compared to the trends of data a few weeks ago, the numbers are substantially lower.  Social distancing has saved lives.  Quite likely hundreds of thousands of lives and perhaps a million have been saved. 

It may very well be that our large, diverse, and patchworked-policy country cannot be modeled as a single unit.  An alternate and far more complex and intensive effort of modeling regions, states, and cities independently could produce better results.  On the other hand, the data from some states are extremely noisy, not just on the weekends.  One of the lessons in all of this is that few if any of the State Health Departments were ready to archive and distribute data.  This goes hand in hand with the lack of testing.  This same criticism goes ten-fold at the federal level.  My impression is that the states are making tremendous progress while the federal government continues to flounder.  I'm quite sure everyone is working overtime to do the best they can.  This is not a failure of people, but a failure of leadership.  Something to remember at the next election.

UPDATE:

The following unconfirmed story suggests that testing has suddenly dropped by up to 30%.  If true, this might (emphasis on might) explain why I am no longer able to fit a single curve to the data.  If the recent data has suddenly suffered from a 30% drop, the apparent stabilization and slight decrease in cases may be fictitious.
https://www.politico.com/news/2020/04/14/coronavirus-testing-delays-186883

COVID-19 April 14, 2020

Today should be a very interesting day.  Will the low weekend numbers bounce back as they have in the past? If so, by how much? Today's numbers should be highly indicative of when the "peak" will occur.  If the numbers today and tomorrow don't give a substantial upward bounce, I will have to readjust the model curves (and that's a good thing). And so we wait!

COVID-19 April 13, 2020

Nothing all that new today.  The weekend number bias was in full force, as you can see in the data below.  The daily death rate chart and the daily new cases chart really show it well.  I suspect we'll see things increase over the next few days. 

I have tweaked the Gompertz parameters a bit.  I'll wait a few more days before I report on that in detail.  I'm currently finding that we will have a peak in daily deaths of 3420 per day around April 27.  A peak in new daily infections will occur around April 18 at 38,623.  As usual, these numbers are highly uncertain, so take them all with a large grain of salt.

COVID-19 April 12, 2020

Happy Zombie Day everyone. I'm only going to post the current charts. No real analysis today. The weekend data glitch seems to have arrived on schedule. I expect artificially depressed numbers today and probably on Monday as well. Then numbers will increase as the weekend backlog is unjammed.