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Coronavirus Graphs by Country, as of 3-16-2020
As a public service, I’m going to post a few WuFlu graphs by country, as a follow up to my prior posts over the weekend. I plan to update these every couple of days.
For the moment, these graphs will compare reported cases in South Korea, Italy, France, Germany, Spain, the US, and the UK. I’m going to exclude China and Japan for the moment, as there appears to be little increase in these countries.
These graphs will show daily progression, starting when each country first surpassed 200 reported cases. This appears to provide a good comparison of the progression between countries. I also prepared similar graphs starting when each country first surpassed 1,000 cases, and the results weren’t notably different.
In each graph, I also include a line showing an exponential growth curve, assuming 33% daily growth. As you will see, this models the progression well in the early period (around the 2 weeks after each country reached the 200-case threshold), but significantly overstates the growth thereafter.
Here is the first graph, in a linear scale. Note that the exponential curve is truncated at day 19 (the red line; more on this later).
It’s hard to differentiate the countries in the first 10 days or so. You can see that most are pretty close to the 33% daily growth line through day 12-13, with Spain a bit higher and the UK a bit lower.
A logarithmic scale makes it easier to differentiate the numbers in the first 10 days or so. Remember that a logarithmic scale uses increasing increments as one moves up the y-axis — so in the graph below, the first increment is 900 (from 100 to 1,000), the second increment is 9,000 (from 1,000 to 10,000), and so on. Exponential growth appears linear when using a logarithmic scale.
On this graph, a downward curve indicates that the daily growth rate is declining. This can occur even while the daily number of cases is increasing. The downward curves apparent in Italy (orange) and S. Korea (medium blue) are good news. Even Spain (light blue) appears to be curving downward a bit.
One final graph, to demonstrate the magnitude of the error of doing what many people are doing — including, apparently, many of the experts. This graph is the same data as the original graph above, in linear scale, but I have not truncated the 33% exponential growth projection.
You can see that if you carry out the 33% exponential growth projection to the end of the graph, it vastly overestimates the number of cases. Focusing on Italy and S. Korea:
- For S. Korea, now on day 25 after surpassing 200 cases, the actual number of reported cases is 8,236. The 33% exponential growth projection is 187,702. The exponential growth model overstates actual S. Korean cases by more than 22 times.
- For Italy, now on day 22 after surpassing 200 cases, the actual number of reported cases is 27,980. The 33% exponential growth projection is 79,784. The exponential growth model overstates actual Italian cases by 185%. Note that for Italy, the exponential growth model appeared pretty accurate through day 14 (March 8, 2020, for Italy), which was only nine days ago.
My final comment relates to the good news out of Italy, which reported just 3,233 new cases yesterday (March 16). This was a slight reduction in the number of new cases from the prior two days, but a significant reduction in the percentage rate of increase. For the five days between March 10 and March 15, Italy’s growth rate in reported cases was 19.5% per day. For March 16, it was only 13.1%.
Daily reports can vary for a variety of reasons, so we should not immediately conclude that Italy has turned the corner. But it is encouraging news.
Stay tuned, God bless, and fear no darkness.
Published in Healthcare
The change in the rate of growth is the second dirivative? Like acceleration/deceleration in your car.
Great analysis. A couple of points, both Spain and the UK have stopped testing for mild symptoms cases. Not sure what they are doing in Italy, but if trends continue over there, is pretty good news. Probably the most reliable data set in terms of actual infections is the one from South Korea, due to the larger screening they did over there (as far as I know).
Yes, the change in the rate of growth is the second derivative of the number of cases. On the graph, it appears as an “inflection point.” S. Korea’s inflection point was around day 12. My impression is that Italy just passed its inflection point, over the weekend, though it’s hard to tell until we have a few more days of data.
Math can be beautiful. I wish I knew statistics better. I think most Americans are not very well versed in the math of large numbers, (I read a book about that). A professor once asked the class to mark where 1 million was on the chalkboard using zero on the left and a billion on the right. Most put the mark in the middle. We are talking billions of people and trillions of dollars. Our newscasters and political advisors (1 million to each American from Bloomberg, and 500 million people go bankrupt refered to by Sanders campaign) , both blatant errors of magnitude. Their opinions should be discounted without their acknowledgement of error, straight up without excuse.
If you are looking for racism, it isn’t far that you find a racist, Peter Thiel once said. If you are looking for a disaster, you’ll find that too. The continued rate of exponential growth just doesn’t happen until everyone is dead. I like the use of what information we have, with what has happened in the past. Empirical evidence is helpful.
Everything overlaps, like one of those transparent images of the bones, muscles, nerves, cirulatory systems my parent’s encylopedia had contstituting one body. Very complex and effieciently run when healthy.
This time, Elizabeth, it’s the big one!
The upshot from the OP: The projection of a 33% daily increase is wrong and way overstated for Italy and S Korea. Don’t panic.
Our fixation here on the 33% daily increase goes back to a chart supplied by Kozak and identified by Drlorentz as coming from this Financial Times (FT) article. There they claim, “In most western countries case numbers have been increasing by about 33 per cent a day, a sign that other countries may soon be facing the same challenge as Italy.” They’re not wrong.
Note the FT graph starts tracking cases beginning the day a country has its 100th case. In the OP, the origin of the horizontal axes of the graphs is the day it exceeds its 200th case. But no matter.
Again the FT isn’t lying when it claims cases have been increasing about 33% daily in the western world. Italy runs along the 33% daily increase line (the broken line) till about day 15, then starts dropping below it after. Spain is above the 33% line up to day 14, as is the US up to day 12. Germany and Switzerland are tough to see, but the graph shows they lie along the 33% increase line until days 15 and 11 respectively. Those days I mention are also the stopping points, which is basically the most recent date for which the graph has data, March 16.
The problem with the OP and its accompanying graphs is an important omission–by no means Jerry’s fault because the graph that started this all was a simplified version of the FT graph above. Jerry’s right to rejoice that Italy and S Korea show a country’s trajectory can fall below the path of a devastating daily 33% increase.
The original FT graph provides additional info on the public health measures undertaken by the exemplary cases of East Asia. Besides S Korea, Singapore, Japan, and HK are well below the 33% panic line.
I replicate Jerry’s first graph just for Italy and the 33% panic line. Two differences: I specify actual dates on the x-axis and add two red lockdown lines.
Italy doesn’t drop below the 33% daily increase line until after varied closures and “extreme” lockdowns take effect, beginning with the Feb 22nd quarantine of over 50,000 people in 11 municipalities in Lombardy. On March 8, all 16 million people in Lombardy are quarantined and on March Mar 13, the all Italy goes into lockdown.
Consider now how aggressive measures must be in New York state (pop 19M) or Washington (pop 7.5M) or the US in the aggregate to bend that curve. Consider too how the US expects to fare given its testing fiasco, relative to South Korea’s outcomes which were built on early and aggressive testing (including the asymptomatic). The Italian experience teaches us they’ve had to resort to regional and national lockdowns to drop below that 33% daily increase trajectory.
Finally, as to the OP’s third graph and point that it is simply fearmongering to project a 33% daily increase, the original FT article doesn’t claim that. Also it’s basic statistics not to extrapolate beyond one’s data. The original FT graph doesn’t do that. It’s describing recent history, not projecting the future. It traces the paths of countries up to the date for which there are actual data. So far case growth has been roughly at 33%. Whether they continue on that path depends on the efficacy of their responses.
cases != diagnosed cases != confirmed cases. Untested people and false positives require more precise definitions.
You’re welcome to do the work and draw out the implications. I’ve done my bit to clarify. I go no further.
Good points, though I very much doubt that the lockdown was effective as quickly as suggested by this graph. The reported incubation period is 2-14 days, so it seems unlikely that a lockdown is going to help much within the first week or so. I do realize that you note a small lockdown in some of the Italian cities on Feb. 22 that is not shown on the graph.
It’s hard to tell how much of an effect that lockdown is having. I think that it is an error to attribute the decline to the lockdown, as post hoc ergo propter hoc is a logical fallacy. But I do not dispute the proposition that a lockdown can help. I cannot evaluate effectiveness without significantly more information than I have.
The FT article is behind a paywall, so I’ll have to take your word that it does not make a projection.
A great many people are making projections. Here is a story at NY Magazine, just 4 days ago, claiming that a CDC model projected 160-214 million US cases over a period of more than a year, with 200,000-1,700,000 deaths. The same story cited an estimate by Dr. James Lawler (at U. Nebraska), projecting 96 million US cases and a death toll of 480,000. I don’t see how you could get to such figures, without a long period of exponential growth.
Now that’s something I do know about.
It’s not a fallacy.
It’s a pattern of reasoning that is often used fallaciously.
See here for more on that.
You cite yourself almost as well as ol’ Jack Burton. :)
I think that you’re incorrect, but this depends on the definition of fallacy. I don’t have a logic text handy, but my recollection is that a logical fallacy is an invalid argument, meaning an argument in which the conclusion does not necessarily follow from the premises. It is possible for a fallacious argument to have a correct conclusion.
For example: Everyone over 5’11” is an American. I am over 5’11”. Therefore, I am an American. The argument is a logical fallacy, though the conclusion turns out to be correct.
But perhaps this is the type of pedantry up with which you will not put, especially in the midst of the Kung Flu Pandemic.
Yes, it depends on the definition of fallacy, and fallacious arguments can have false conclusions.
A fallacy is an error in reasoning. (I think that’s more or less what you’ll find in the textbooks and the dictionaries.)
You’re using the technical definition of an invalid argument, but invalid arguments in this technical sense are only fallacious if you’re trying to make valid ones–ones where the premise would, if true, absolutely guarantee the conclusion.
Merely probabilistic arguments are frequently not fallacious.
Where’s the fallacy? That’s a good syllogism. It just has a false premise.
Oh, this is great stuff.
That’s good. I wish I hadn’t missed it back then.
There’s a bit of good news just in from Italy. Worldometer has updated their figures for today (Mar. 17), and Italy is now reporting 31,506 total cases, up 3,526. That’s a slightly higher number of new cases than Mar. 16 (3,233), but the percent increase is down again, to 12.6%.
Spain’s report for Mar. 17 is also encouraging, up just 18.9%. I know that this sounds like a lot, but the average for the preceding 5 days had been 34.3%, so this is a significant drop.
Remember that we would expect there to be some “noise” in daily figures, so we shouldn’t read too much into a single day’s result. But it’s nice to see good news from the two European countries that have faced the most difficult time thus far.
I’m gonna go outside and sing the EU Anthem. Except that I’ll sing the English version, Hymn to Joy.
Jerry: Great post. I’d be even more interested to see a comparison of daily deaths on a logarithmic scale. I’m almost certain the separation from the Italy curve would be dramatic, since Italy’s death/case is the highest on earth.
Our early spike of Seattle nursing home deaths distorts our stats at this early stage (making our death rate worse than it’s likely to be, and making a misleadingly good bend in our logarithmic daily death curve) , but it’ll be interesting to track our curve in the coming week or two as a more reliable pattern emerges.
What’s fascinating about a logarithmic curve is that you can start to project a ballpark endpoint in a way that is difficult with an arithmetic scale. Italy looks to be bending toward 10,000-25,000 total dead. We might be able to make very rough US projections of an endpoint in a few weeks — certainly to the nearest power of ten. Normally such a margin of error would be of little use, but given how widely opinions vary on this matter, getting the correct power of ten would narrow things down quite a bit.
That’s a good enough idea to convince me to do it:
I left out S. Korea, which has very few deaths. The tricky question is when to start the count — I used the same dates as in the OP, i.e., the day on which each country surpassed 200 reported cases.
As you can see, Germany is doing very well. Spain is actually on a worse track than Italy. The US trend is pretty favorable.
Remember that this is a logarithmic scale. Italy has 2,503 reported deaths; Spain 533; the US just 112, so far.
Jerry thx that’s awesome! Starting the US post-Seattle-noise helps too.
These curves are the whole ballgame in my opinion since so much of the “daily new cases” discussions are often unwittingly just “daily ability to detect new cases” discussions.
How many will die? — That’s what we all want to know but don’t. This helps and will point to the (very approximate) answers sooner than most people realize.
I’ve been thinking the same thing. I wonder how much of each day’s increase in cases is explained by more extensive testing, especially in the US. At the very least, it seems like somebody could tell us:
That wouldn’t answer the question, but it might help us make an educated guess.
Dr. James Lawler case is US not worldwide? I thought his numbers were worldwide?
That is the reason S. Koreas numbers are maybe the best set. They had good testing numbers of mild cases. The death rate/Critical/Hospitalization ratios would be overstated if the mild cases are undercounted. Which to me has to be a lot higher than false positives. However I don’t know the data on Flu testing in regards to false positives.
The Lawler estimates are for the US. Here are the slides. The estimates are on page 9.
Yes, I agree. False positive are certainly small compared to overall uncertainty at this point.
South Korea. I read a summary of a preliminary paper somewhere suggesting there are some genetic elements to the rate or severity of infection making East Asians particularly susceptible. I haven’t kept track of whether that’s held up, but it would make extrapolating from South Korea challenging.
I suppose infection rates for diseases like this are always estimated, since virtually nobody is tested. Maybe they use surveys or something. That wouldn’t separate corona virus from other strains of the flu, though. You’d need some sampling, which is probably not anybody’s highest priority at this point.
It goes to Dr. Wogard’s point that we’re currently making a lot of assumptions about how this year looks relative to a typical year with respect to corona virus.
See here for US testing data and the researchers’ caveats.
BREAKING: Italy reports 4,207 new cases of coronavirus and 475 new deaths, raising total to 35,713 cases and 2,978 dead.
Despite national lockdown (and more extensive testing than the US by the way).
So again let me put the question: how do people think these trajectories would develop minus measures like social distancing, closures, and entire lockdowns?
Hard to say. I would bet money that those measures help some. But how much is another question. Even more difficult is the question of whether the benefit is worth the cost. I’m waiting for some more hindsight to show up.
I’ve been following the data from Johns Hopkins here. It looks like there will be no flattening of the curve today for cases outside of China, unless we’ve already had the last update for the day. But there will probably be one more update. (Strictly speaking, I shouldn’t say no flattening of the curve. I should instead say no slowing of the rate of increase.)
Snirtler, I don’t think that anyone knows the answer to your question. I sure don’t.
S. Korea did not lockdown, and has followed a very favorable trajectory. They did other things, and I do not have the data the might be necessary to assess the effectiveness of their actions.
The latest from Italy is not bad news, though it’s not favorable either. The 4,207 new cases that you report (for today, Mar. 18) is an increase of 13.4%. This is slightly higher than the prior 2 days (13.1% and 12.6% on Mar. 16-17), but not a significant increase in the rate.
As I noted previously, due to the incubation period, it seems unlikely that we would see a benefit from a “lockdown” until about 1-2 weeks later, and the main Italian “lockdowns” were on Mar. 8 and 13 (per your chart above). Rates were trending down in Italy before I would expect the lockdowns to have affected the numbers, but perhaps we’ll see further improvement over the next week or so.
Thanks, Jerry. I continue to watch these numbers hoping for them to go down persistently.
I would be curious to see these numbers/graphs updated over the next several days.