A better COVID-19 graph

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Aatish Bhatia plots COVID-19 data in (a population-growth version of) phase space, eliminating time as a dimension — which turns out to be a good idea, as it often is:

An explanation by Henry Reich:

There are some linguistic connections — viewed abstractly, this sort of analysis connects to pretty much everything — but I'll leave that for another time.


  1. Andrew Usher said,

    April 3, 2020 @ 7:39 am

    A linear relationship (well, almost) is what should be expected – anyone far below it should be strongly suspected of using fake data.

    [(myl) It's not obvious (at least to me) that it should be the same linear relationship across all countries — or all states in the U.S:


  2. colin mclarty said,

    April 3, 2020 @ 7:49 am

    There is not just one thing to understand about covid. So while it is valuable to note this chart eliminating time, it is not *better* than charting the time evolution.

    [(myl) Agreed. But I think Aatish Bhatia is right to suggest that this is a better way to visualize the development of exponential growth across locations, and the extent of local progress in ending the pattern.]

  3. Chester Draws said,

    April 3, 2020 @ 9:47 am

    [(myl) It's not obvious (at least to me) that it should be the same linear relationship across all countries — or all states in the U.S:

    If something appears too good to be true, it usually isn't true.

    If you reversed the purpose of the graph, and used it to find out which countries were lying about their death toll, what would the obvious conclusion be?

  4. Leo said,

    April 3, 2020 @ 10:40 am

    "4/2/20" – also known as 2/4/2020 to some of us, or indeed as 2 Apr 2020 if you want to be as clear as possible.

  5. Greg said,

    April 3, 2020 @ 10:50 am

    The folks expressing skepticism in the comments above seem to be saying that any countries reporting good numbers must be lying. This is a very robust stance to take, as there is literally no way to falsify the claim! Any evidence that one country is doing better than another suddenly gets jiu-jitsu’d into proof that country is lying.

  6. Jonathan Smith said,

    April 3, 2020 @ 10:55 am

    Various countries' total cases against new cases in past week plotted logarithmically must be linear why? It is impossible for anyone's situation to have really changed for the better over recent time? Oh wait, I suppose this is actually the argument and the reason for our new national focus on "hangon China must be falsifying data"…

  7. Jonathan Smith said,

    April 3, 2020 @ 10:56 am

    oops, what Greg said

  8. Barbara Phillips Long said,

    April 3, 2020 @ 2:37 pm

    Graphed profiles presented by Kevin Drum at Mother Jones compare various countries to the outbreak in Italy:


    Look for entries headed “Coronavirus Growth in Western Countries.” For the nonstatistical, there are also cat photos.

  9. AntC said,

    April 3, 2020 @ 7:39 pm

    The folks expressing skepticism in the comments above seem to be saying that any countries reporting good numbers must be lying. This is a very robust stance to take, as there is literally no way to falsify the claim!

    Not necessarily lying; perhaps just (criminally) negligent; or with inadequate public health systems; or without a institutional will to protect the masses.

    I disagree with "no way to falsify". There in most cases is indirect evidence; yes we must treat that with suspicion. We can also look at the logistics of testing and the rate of testing and contact-chasing; and whether they are enforcing isolation.

    Take Indonesia: huge numbers of Chinese tourists in Bali/Lombok over the Lunar New Year, including direct flights from Wuhan. And yet no cases reported for weeks after neighbouring countries (Malaysia, Singapore, Philipines, even Australia) were reporting hundreds. Note that Indonesia's testing labs are on Java, a long way from Bali. And now Indonesia's numbers appear to show a death rate close to 10% of reported cases — even though reported cases are still way below those neighbours.

    So either COVID-19 has some special characteristics in Indonesia — in which case it would help the world if we could find out what; or Indonesia has not been testing so extensively; nor tracing contacts and testing them. Now some of that is hypothesising on my part; but each of those hypotheses are falsifiable — if there was a will in Indonesia to do better.

  10. bks said,

    April 4, 2020 @ 6:59 am

    In the USA now growth in cases is exponential and there is an extreme bottleneck in testing with, e.g., Quest reporting a 160,000 test backlog (samples taken but waiting for RT-PCR). Waits of over a week are common, if one can even get approved for a test. Until the capacity for testing expands faster than the infections, any "drop" in the graph will simply be an artifact of the testing bottleneck.

  11. Andrew Usher said,

    April 4, 2020 @ 9:19 am

    Well, using 'confirmed cases' is a compromise to begin with. Testing might run ahead of demand (which would produce a rise) or behind it (which would produce a fall) or both as is likely in the full course of the outbreak. The logarithmic scale minimises the impact of this (note the range of 100,000 – much larger than any change in testing that is likely).

    k_over_hbarc at yahoo.com

  12. David L said,

    April 4, 2020 @ 2:40 pm

    It's not obvious (at least to me) that it should be the same linear relationship across all countries — or all states in the U.S

    Exponential growth means that the number of new cases (N) is proportional to the total number of confirmed cases (T): N = kT, where the value of k depends in part on the properties of the virus itself, in part on the rate of contact between infected people.

    But the graph is on a log-log scale, so we get log N = log k + log T. In other words, the slope is always one, and the difference between different areas shows up as an offset in the position of the lines. In practice, I would the think the range of values of K would not be great, and then you take the log, so the range would be less. That's why all the lines for exponential growth are approximately on top of each other.

    And as Bhatia says, if the curve in a given area starts to fall below the straight line, then growth is becoming slower than exponential — flattening the curve, as we all know to say now.

  13. Chester Draws said,

    April 4, 2020 @ 9:52 pm

    I'm sorry, I take it back.

    A country known to be economical with the truth is placed on a scatter plot and is a massive (really massive, due to the log nature) outlier. That must mean it is awesome. Doubly awesome, since it isn't even particularly rich.

    The killer proof is how open they are being about letting people talk about it, so they don't have to rely on rhyming emojis or nonsense like that.


  14. Jonathan Smith said,

    April 4, 2020 @ 11:29 pm

    @Chester Sorry to hear U R mad that cases are no longer growing exponentially in China. Don't lose hope tho; things could flare up again there at some point, hopefully after we are done with their ventilators lol.

  15. Andrew Usher said,

    April 5, 2020 @ 12:14 am

    Certainly the China point can't be taken at face value and I don't think that needs further comment.

    Ultimately, of course, every curve will turn down no matter what because the population that can get it is finite.

  16. Rodger C said,

    April 5, 2020 @ 8:36 am

    Chester, you do realize that the Babylon Bee is a satire site? Not that the situation being satirized isn't true.

  17. Rose Eneri said,

    April 5, 2020 @ 9:21 am

    Credible reasons for any outliers must be based on real data. I put no credence at all in anything China reports. Including "data" from China in the graph is just for completeness.

    Although number (especially daily) of confirmed cases might be useful in predicting future cases, it is otherwise not a very meaningful number because lots of infected people have minor or no symptoms. What matters is how many, and for how long, infected people require hospitalization; how many, and for how long, infected people require a ventilator; and how many die. These are the factors that strain medical facilities/supplies and that cause the most human suffering.

  18. Chester Draws said,

    April 5, 2020 @ 8:42 pm

    I'm not mad about the Chinese lying.

    What it will do is keep the travel restrictions to China in place much longer than otherwise. Probably years longer. They're hurting themselves, not us, and that's going to be a major issue for their export industries and foreign investment.

    Openness is actually the best policy in these things. The truth always comes out eventually anyway.

  19. Toby said,

    April 5, 2020 @ 9:47 pm

    @chester is right here. Noone could ever trust anything out of China generally before (GDP figures, stats, quality of manufactured goods, technology, currency manipulation etc) and now its obvious and continuing deceit is only harming itself now.

    The great decoupling has already begun.

    My only fear is that China is preparing its own population with its obvious lies about the CIA etc for a strike on a US plane or ship (like it did in early 2001 in Hainan to test GWB) to destabilise things further (and against that background the captain telling the world a US carrier in the Pacific was essentially disabled was criminally negligent).

    A once great civilisation has been ruined by having a homegrown revolution which installed the dregs of the lower middle class, who succeeded in destroying everything good and beautiful and left a debased barbarian shell which is a threat to world peace and stability.

  20. Andrew Usher said,

    April 6, 2020 @ 6:54 am

    I believe they have done enough destabilisation through the coronavirus, whether intentional or not! The way it's going now, they are definitely getting through this in a better position and there's no need for a military attack.

  21. Ken Kahn said,

    April 8, 2020 @ 6:22 am

    Why this use of confirmed cases instead of active cases (confirmed minus those that recovered or died)?

  22. AntC said,

    April 16, 2020 @ 6:52 pm

    xkcd's graph beats the lot of them


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