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Comparative Coronavirus Case Growth
Yesterday morning, our friend Kozak posted a comment about Coronavirus case growth by country. It included a chart showing case growth in a number of Western nations (Italy, Germany, France, US, Switzerland, UK, and Japan), but not including S. Korea. His impression was that “[w]e are on the exact same trajectory as Italy,” and noted that “Korea quickly moved to identify and isolate cases and do aggressive contact tracing to limit the spread of the disease. As a result, they kept their medical system from being overwhelmed.”
I was skeptical of this, so I did a bit of data analysis on my own. I will copy the graph from Kozak’s comment later on, but I don’t want to bias your impression. My contention is that, at present, it is not possible to tell whether we are on the (somewhat troubling) path of Italy or the (much more reassuring) path of S. Korea.
I did not find daily data for Switzerland, but I was able to easily find it at the Worldometer site (here) for other relevant countries. My methodology was to start data reporting on the first day in which each country reported over 200 cases. The countries, and dates on which they exceeded 200 cases, are as follows:
- S. Korea — 209 total cases on Feb. 21
- Italy — 229 total cases on Feb. 24
- Germany — 203 total cases on Mar. 3
- France — 212 total cases on Mar. 3
- Spain — 228 total cases on Mar. 4
- US — 221 total cases on Mar. 5
- UK — 209 total cases on Mar. 7
Here is the graph, by country, for the first 10 days. Note that this graph uses a logarithmic scale, as did the one posted by Kozak (still to come).
Notice that all six countries follow a very similar pattern. There is little difference, over this period, between S. Korea (medium blue) and Italy (orange), and the US (green) is quite similar to both.
The US is only 9 days into this analysis, with 3,110 reported cases. At 9 days in, S. Korea was at 3,736 reported cases, and Italy was at 3,089.
Accordingly, I contend that based on reported cases to date, it is not possible to determine whether the US is following the trajectory of Italy or the trajectory of S. Korea.
Kozak is correct to note the difference between the experience of Italy and S. Korea. Here is the full graph, through the latest case reports for yesterday (Mar. 14), though I’m switching to a linear scale for this graph:
In S. Korea, there are 22 days of information since it first passed 200 reported cases on Feb. 21, while in Italy, there are 19 days of information since it passed 200 reported cases on Feb. 24.
Note that the linear scale properly displays the significant rate of growth in total cases, especially in Italy. It has the disadvantage of stretching the vertical scale, making it more difficult to distinguish between the various countries at the early stages of the spread of the WuFlu.
Notice the rapid rise of WuFlu in Spain (light blue). Spain appears to be on a trajectory significantly higher than any of the other countries included in this graph. If this trend continues, it would not be surprising if the focus of news coverage switches from Italy to Spain in the next few days.
Based on my (admittedly limited) research in the area, epidemiologists generally expect the number of cases to follow an “S-curve.” The S. Korean figures follow this curve — an initial, rapid increase that appears to show exponential growth, but reaches an inflection point, after which the rate of increase declines and approaches an asymptote. For many such S-curves, the inflection point appears to occur at about half the level of the asymptote.
For S. Korea in particular, the inflection point appears to have occurred around Day 11 or 12 (Mar. 3 or 4), when the total number of cases were 5,186 and 5,621, respectively. This suggests that S. Korea’s asymptote will be around 10,000 to 11,000.
With this explanation, here is the graph posted by our friend Kozak yesterday (here, comment #21). Again, I emphasize that this is not Kozak’s graph, but is (presumably) something that he found online:
I have several criticisms of this graph. First, notice that it does not include S. Korea, but does include Japan. Inclusion of S. Korea — as shown in my initial graph above — demonstrates that the other countries are on a trajectory that cannot be distinguished from that of Italy or S. Korea. However, the inclusion of Japan gives an inaccurate impression that the progression of the WuFlu in Europe is significantly different than in Asia. This impression would have been eliminated by the inclusion of S.Korea in the graph.
Second, note the inclusion of a “33% daily increase” line. This line is characteristic of exponential growth. Notice that it appears to be a straight line on this graph, because of the logarithmic scale.
Third, note that this graph includes data only through Mar. 9. This is not inherently deceptive. To the contrary, I assume that the graph was prepared around Mar. 10 or 11, with the latest data available.
However, the design of the graph above gives the inaccurate impression that ongoing, 33% daily growth is what we should expect from WuFlu.
This is not true even of Italy — though through Mar. 9, and especially if we use a logarithmic scale, it appears to be pretty accurate, as shown by the graph on the right.
I have calculated the daily growth rates for reported WuFlu cases in Italy, over the past 22 days, with the following averages:
- Feb. 24-Feb. 29 (5 days): Daily increase 37.5%
- Feb. 29-Mar. 5 (5 days): Daily increase 27.9%
- Mar. 5-Mar. 10 (5 days): Daily increase 21.3%
- Mar. 10-Mar. 14 (4 days): Daily increase 20.2%
Note the decline in the percentage rate of increase, which is what we would expect from an S-curve, but not what we would expect from an exponential curve.
If you’ve read this far, I thank you for your attention. The big reveal is coming.
Looking at the last couple of graphs: the one from Kozak’s comment, and mine, both seeming to show that a 33% daily increase is a reasonable projection for the growth of WuFlu in Italy — and, by extension, for the US and other countries. But here is how the 33% daily increase graph compares with the actual number of reported cases in Italy through yesterday, Mar. 14, using a linear scale:
See the problem?
An estimated growth rate that seemed perfectly reasonable just 5 days earlier, particularly when viewed on a logarithmic scale, is revealed to be completely wrong.
The estimate for Mar. 14 for Italy, using the 33% daily growth model, is 51,644 cases. The actual number of reported cases in Italy, as of Mar. 14, was 21,157.
Thus, the 33% daily growth model, suggested by the graph posted just yesterday by Kozak, is already overstating cases in Italy by 144%, just 5 days later.
I want to emphasize, again, that my goal is not to pick on Kozak. We have very poor information about what is going on, and this seems true even for medical providers.
I have very little idea how the WuFlu is going to progress. I am quite confident that it will not progress with ongoing 33% daily increases, as shown in the graph on the left.
Just eyeballing this graph, and assuming that the number of cases is going to follow an S-curve, it appears that Italy is probably pretty close to its inflection point. If today is the inflection point, we’d expect a total of about 40,000-45,000 cases. Perhaps it will be a bit higher, both in Italy and elsewhere.
As noted previously, I’m particularly concerned about Spain, if its present trend continues.
It would be helpful if the authorities would release some sort of reasonable projections. What we are getting are “worst-case scenario” projections — like this from Dr. James Lawler at an American Hospital Association webinar on Feb. 27, projecting 96 million cases and 480,000 deaths in the US, or this reporting yesterday on a CDC projection of 160-214 million cases over the next year in the US, and 200,000 to 1,700,000 deaths.
What I worry about is that these projections are like the 33% increase projection debunked above with respect to Italy.
Time will tell, I suppose. God bless, everyone, and fear no darkness.
Published in General
A point a lot of people miss. Variables. . I also find a lot of the charts look scary because the y axis is a small number, if total population is used the curve would look rather flat. I do think this is a real virus, but some of the projections won’t be.
Read on another blog the Spanish flu hit 20% of the population, which was similar to the crusie ship that was held up for 2 weeks, where passengers mingled, so perhaps at the high end a 20% infection rate may be closer this round anyway.
Your wish is my command. This time only. :)
This graph shows total reported WuFlu cases in the US from Mar. 5 to Mar. 15. Consistent with my prior analysis, I start on the date when US cases exceeded 200. The 35.1% line shows exponential growth. I didn’t pick 35.1% at random — rather, this is the actual daily growth rate for the first five days of this ten day period. If we had done this analysis on Mar. 10, and assumed exponential growth, 35.1% is the figure we would have used. And it would have been wrong, by a factor of 21% after just 5 days.
The overall daily growth rate, for this ten day period, is 32.5%. The average was 35.1% for the first 5 days, and 29.9% for the second 5 days. The tendency, from other countries, is for the daily growth rate to continue to decline.
This can occur even as the number of new cases reported daily increases significantly. As an example — if you have 40% daily growth from 500 cases, the number of new cases is 200; if you have 20% daily growth from 3,000 cases, the number of new cases is 600.
I’ll probably continue to monitor these results, now that I’ve become so obsessed with the calculations.
My post evaluated whether we might be following the trajectory of Italy, or of S. Korea.
There is a more troubling possibility, because we are a much bigger country. S. Korea has about 50 million people, and Italy about 60 million. Our population is 5-6 times higher than these, so it is possible that we could follow a track similar to Italy times 5. That would be quite a bad result.
So far, the progression in the US remains similar to Italy (though about 10 days behind).
OK, teacher said there are no dumb questions. What is the distinctive symptom that distinguishes this virus from other flu viruses?
I am told that the key symptoms are difficulty breathing, a dry cough, and a fever.
Boy, that’s just about useless, isn’t it?
That’s not a criticism of you, Spin. But basically, any of these 10 symptoms may be indicative of the WuFlu.
I have a headache at the moment, and I sneezed twice this afternoon. Should I go to the hospital?
So, basically everything is Coronavirus.
There is only one useful indicator on this list which is shortness of breath. That is the only one that should send you to the hospital. Otherwise stay home.
Yeah, I know. I am in Washington State, and we are just assuming anyone that looks cross-eyed has it.
Summary: The first derivative is still greater than 0 while the second derivative is not zero but less than 0.
So it is still frightening. What is going (or not going on in Mexico) should be of real concern especially for you in the south west. It could be a real source of tertiary infection in the US. China was primary. EU secondary. Mexico tertiary.
I see 53 cases and no deaths in Mexico, according to the Johns Hopkins map. Is that what you’re referring to?
Mexico is dismissing the entire thing at the moment. They had large gatherings over the weekend and were taunting the US. Especially Mexico’s president.
Interesting. I hadn’t known that.