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.
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
1 comment:
Interesting post regarding testing dropped by 30%. Awful and I tend to trust most of Politico's reporting. Also, yesterday, we saw a dramatic uptick. We can expect the same today and the flattening isn't all that genuine. Also, we're seeing those spikes within areas, i.e. looks like South Dakota is potentially the next hot spot, con
I fear this is going to give many people a false sense that we're over this. I fear that it will embolden those who are against social distancing because it infringes on their 'constitutional rights' much like we saw recently in Michigan.
Overall this has been a piss poor response. It doesn't matter if you are the most powerful nation and wealthiest nation if you have piss poor leadership. I've seen many managers come in and wreck a perfectly functioning department.
As always, thanks for your analysis. I look forward to your updates much like I look forward to hurricane tracking during the season and swell tracking when I lived in NorCal.
Take care and stay safe
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