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New Bloomberg Column: This is Not The Flattened Curve We Were Promised
April 17, 2020
An empirical observation about models versus reality:
This Isn’t the Flattened Curve We Were Promised
See other columns I wrote here.
Categories: Uncategorized
mathbabe 
Re “If people stick with measures to contain the virus, death rates will eventually trickle down to zero, but only after almost everyone has been infected, assuming they are then immune.”
My understanding is that once a pandemic goes sub-critical (which it looks like it has)
the number of people infected (i_\infty) is mostly a function of the number infected
when it goes sub-critical and how quickly R_0 is declining, not the overall population. If people were more careful, for example, avoiding indoor shopping, wouldn’t we achieve a Wuhan style “other side of the curve”?
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Yeah maybe. Depends on what almost means. What do you think will happen given our current practices?
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We seem to be sub-critical by a little bit already, so if we continue like this (which we can’t in the long term, I know) we’ll see another 100K deaths but not anything like the 2M we’d see if “almost everyone got infected”. There is a lot of mis-representation about i_\infty in the media. A lot of depictions of “flattening the curve” have the same i_\infty before and after flattening, or even worse i_\infty than if the curve wasn’t flattened, but i_\infty decreases with R_0, and especially, has a discontinuity at R_0 = 1.
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Ok I’m glad to be corrected on this. Mostly I just wanted to point out the strictly empirical observation that the curve is by no means symmetric. Happy if it descends faster of course.
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This is a really important observation; the asymmetry between disaster and recovery appears to be a property of unexpected disasters. It is also observed in Talib’s “Black Swan” and will likely apply as well to economic recovery (not at all a V curve but more likely the Nike swoop.) I found it very enlightening to see it in the so-called flattening of the confirmed instances and deaths curves. Thank you.
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Makes sense. The point of flattening as I understand it is (in personal terms) to improve my chances of surviving an infection, by buying time for hospitals to get enough ventilators etc., rather than to reduce my chances of getting infected sooner or later. Being in the higher-risk category by age, I’d just as soon stay in lock-down for a year or two with the protection of a vaccine.
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I agree! I am in lockdown to give the hospitals and first responders time to acquire the necessary equipment. I am also 70, and already used to staying home.
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Great article. Please keep looking at the numbers.
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Curious, I looked up how many months the “curve” covered for the 1918 influence pandemic lasted. All I found was “it spread worldwide from 1918 -1919. … it was first identified in military personal in spring 1918.”
https://www.cdc.gov/flu/pandemic-resources/1918-pandemic-h1n1.html
History.com said, “At the time, there were no effective drugs or vaccines to treat this killer flu strain. Citizens were ordered to wear masks, schools, theaters and businesses were shuttered and bodies piled up in makeshift morgues before the virus ended its deadly global march.” …
“The first wave of the 1918 pandemic occurred in the spring and was generally mild. The sick, who experienced such typical flu symptoms as chills, fever and fatigue, usually recovered after several days, and the number of reported deaths was low.
“However, a second, highly contagious wave of influenza appeared with a vengeance in the fall of that same year. Victims died within hours or days of developing symptoms, their skin turning blue and their lungs filling with fluid that caused them to suffocate. In just one year, 1918, the average life expectancy in America plummeted by a dozen years.” …
Ahh, here the answer: “By the summer of 1919, the flu pandemic came to an end, as those that were infected either died or developed an immunity.”
https://www.history.com/topics/world-war-i/1918-flu-pandemic
From the spring of 1918 to summer 1919, a little more than a year to run its course killing 20 to 50 million people around the world and 675,000 in the United States.
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Since the infection process is naturally geometric, in order to get a symmetrical curve you would need to have R(-t) = 1/R(t) (where R(t) = the number of new people infected by each new case at time t, assuming the peak occurs at t=0), right? (e.g., if we went through a period when new infections were doubling, we would need to go through a symmetrical period when it was halving to balance it out.) So if we started out around R=2.3, we would need to get down to R=0.435 to balance it symmetrically. Which probably reinforces your point – even if we get subcritical, we’re probably not getting down to that level quickly.
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