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  • Hey, this is Henry (from MinutePhysics), and you won’t be surprised to hear that I’ve

  • recently been thinking a bit more about epidemiology than physics.

  • When I see daily news reports on COVID-19 [onscreen show total case numbers: “now

  • 15000 cases in NY state!” etc], it’s really difficult for me to build a coherent picture

  • of what’s actually going on, because the numbers are changing so quickly (which is

  • exactly what you expect with exponential growth) that theyre almost immediately out of date.

  • We know that epidemics tend to grow exponentially at first, and also that exponential growth

  • is really really hard for our human brains to understand because of just how crazily

  • fast it is. My friend Grant Sanderson has a great overview video about exponential growth

  • which I highly recommend.

  • But regarding the news - I’d rather know where were headed, and if were making

  • detectable progress. Are we winning or losing?

  • Because of course, we can’t have exponential growth forever - at some point the disease

  • will run out of new people to infect, either because most people have already been infected,

  • or because we as a society managed to get it under control. But - and this is the scary

  • part to me - when youre in the middle of an exponential, it’s essentially impossible

  • to tell when it’s going to end. Are we in for 10 times as many cases as we currently

  • have? Or 100 times as many? Or 1000? Exactly when exponential growth ends is important,

  • because it hugely determines how many people fall ill, yet so little reporting actually

  • focuses at all on how to tell if exponential growth is ending (which would be a super positive

  • sign!).

  • After talking about this with my friend Aatish, he put together a new - and very useful - animated

  • graph visualizing the COVID-19 epidemic on a global scale.

  • This graph shows all countries travelling along the trajectory of exponential growth,

  • and it makes it super obvious which ones have managed to stop the exponential spread of

  • disease - they plummet downwards off the main sequence in a way that I find super compelling.

  • And this figure also makes it abundantly clear that, even if a country doesn’t have lots

  • of cases right now, covid-19 is probably going to follow this same trajectory there and end

  • up spreading & spreading & spreading - until that country hits the emergency eject button.

  • If youre planning for the future and your country doesn’t have a lot of cases yet,

  • it’s nevertheless a safe bet that youre probably headed down a similar path.

  • So how did we make this graph? Well, there are three key ideas: the first is to plot

  • on a logarithmic scale, since that’s the natural scale for exponential growth - note

  • that the tick marks grow by multiples of 10, so 10, 100, 1000, rather than 10, 20, 30.

  • This scales up small numbers and scales down large numbers, making the growth equally apparent

  • on all scales, and lets us compare the growth in countries with very different numbers of

  • cases.

  • Which brings us to the second idea: catch changes early, by looking at change itself.

  • For example, if you look at the growth of cases in South Korea, you can see that at

  • first theyre exponential, and later, the growth slows down. But when youre halfway

  • up this curve, it’s hard to tell by eye that it’s slowing down - it still looks

  • exponential. If instead you instead chart the number of new cases in the last week,

  • in other words, the rate of growth, it’s much easier to see that the growth is starting

  • to slow down. When the number of new cases each week flattens out or goes down, youve

  • escaped the (scary) exponential growth zone.

  • The third idea behind our graph is one from physics: don’t plot against time. Usually,

  • when you see exponential growth, the number of cases is plotted versus time. But the spread

  • of the disease doesn’t care if it’s March or April; it only cares about two things:

  • how many cases there are, and how many new cases there will be - that is, the growth

  • rate. The defining feature of exponential growth is that the # of new cases is proportional

  • to the # of existing cases, which means that if you plot new cases vs total cases, exponential

  • growth appears as a straight line. So these are what we plotted on our graph: the number

  • of new cases (aka the growth rate) is on the y axis, and the cumulative number of cases

  • is on the x axis, both on logarithmic scales. [visual footnote on the graph about cumulative

  • vs current # of cases]

  • This gives us a beautiful-horrible graph that shows where all countries are in their COVID-19

  • journeys; it makes it obvious that the disease is spreading in the same manner everywhere

  • - were all headed on the same trajectory, just shifted in time; and it makes it obvious

  • where public health measures like testing, isolation, social distancing, and contact

  • tracing have started to beat back the disease, and where they either aren’t working or

  • haven’t had time to show up in the data. [graph with animation]

  • In nearly every country (*so far), the number of cases grows at a roughly similar rate,

  • until it doesn’t. And that’s what I feel like is missing from so much COVID-19 coverage:

  • a sense of whether or not we can see the light at the end of the tunnel. Are we still on

  • the rocketship of contagion, or have we managed to hit the emergency eject button?

  • And this graph does that; it gives us some sense of what’s actually happening in these

  • uncertain times.

  • That said, this graph also has a number of caveats & limitations - its main goal is to

  • emphasize deviations from exponential growth - that is, to amplify the light at the end

  • of the tunnel, so it may be less informative for other purposes.

  • [Logarithmic scales distort] 10,000 looks really close to 1,000 on a log scale; this

  • kind of distortion might allow people to take COVID-19 less seriously. Also, the log scale

  • on the x axis makes it harder to see a resurgence of new infections after a significant downturn

  • -- a normal plot compared with time is better for that.

  • [Time is implied] Also, unlike most other COVID graphs youve probably seen, time

  • isn’t on the x axis, which might be confusing! Instead, time is shown through an animation.

  • [“Confirmed Cases” =/= Infections] Another important caveat is that this graph (& basically

  • every other COVID-19 graph that youve seen) is not actually showing the true number of

  • cases, just the number of detected cases. The true number of cases is unknown but certainly

  • much higher than the number detected.

  • [True Growth Rate vs Tested Growth Rate] In reality, COVID-19 cases spread at a slower

  • rate than what the data implies. It’s a subtle idea, but the data reflect not just

  • an increase in cases, but also an increase in the number of tests performed.

  • [Imperfect Data] The data were using is incomplete, as it relies on daily reports

  • from overburdened healthcare systems around the world. Also, different countries have

  • dramatic differences in the resources that are available or dedicated for testing.

  • [Slightly Delayed] Finally, the trends in this plot are delayed a few days, since were

  • plotting the average growth rate over last week (there’s too much variability in the

  • data to plot daily growth rates). This is actually kind of a good thing - it means that

  • it’s a pessimistic graph, it doesn’t get too excited too soon, and so a downward trend

  • on the graph is much more likely to be a real downward trend.

  • And a real downward trend is what we want, for all countries!

  • A lot of the daily news just reports recent data points. Yet to understand where were

  • headed, it’s not enough to know just where we are today - we need to be talking about

  • the trends: how many new cases there are today relative to the number of new cases yesterday,

  • or last week. Charting the rate of change empowers us all to more clearly see what the

  • future holds.

  • A giant thanks to Aatish Bhatia who helped create the interactive visualization, and

  • write this script - Aatish’s work has been a beacon to me in these hard times. And this

  • video was made possible by Brilliant.org, which, I don’t know if you know anyone who’s

  • looking for interactive online math & science resources, courses, practice problems, and

  • daily puzzles right now, but Brilliant.org is the place to go. They cover lots of K12

  • and college level subjects ranging from Fundamentals of Algebra to Calculus to Differential Equations,

  • and of course they have sections on exponential and logistic growth! The first 200 people

  • to go to Brilliant.org/minutephysics get 20% off a premium subscription to Brilliant, with

  • access to all of Brilliant’s courses, quizzes, and puzzles.

Hey, this is Henry (from MinutePhysics), and you won’t be surprised to hear that I’ve

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B1 中級 新型コロナウイルス 新型肺炎 COVID-19

COVID-19に勝っているかどうかの見分け方 (How To Tell If We're Beating COVID-19)

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    林宜悉 に公開 2021 年 01 月 14 日
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