Friday, March 13, 2020

Great Explanation: Exponential Curve V. Logistic Curve

I got this video (below) from Zerohedge ("One Billion Infected In 81 Days?" - Explaining Exponential Growth & Epidemics) but it works very well in a standalone setting. I heard a version of this explanation for how epidemics grow--and slow--early on, but I forgot where I heard it and wasn't sure I could explain it adequately. The video is done by a math guy, so it starts out technical. However, he tries to keep it simple with animated charts, and he gets down to practical answers by the end--which is only a little over 8 minutes from the beginning.

The basic idea is that in any outbreak of an infectious disease with high transmissibility the initial growth tends to accelerate into exponential increase--a very scary thing. That's how you could theoretically wind up with One Billion Infected in 81 Days. However, that exponential increase tends to run up against a number of countervailing factors. One obvious example is that once a given population is saturated, the rate of infection must slow--even drastically. That event--when exponential rate of increase slows--is the "inflection point" when the exponential curve transforms to a "logistic curve": logistical considerations take over.

This can happen naturally, when the population in question is somewhat isolated. That's not the case with China--Chinese travel the world, and we're seeing the results of that in a now-declared pandemic in which centers of infection are thousands of miles apart. However, this transformation of the exponential curve can also be induced by human action, especially by social isolation--removing potential new subjects of infection from the risk zone. Travel restrictions are another obvious way to create an inflection point, as well as medical treatment. There are other considerations, but it should be obvious that it's very much in our interests to induce an inflection point as quickly as possible.

When the Chinese authorities saw--in late December--that the new virus they had first identified in mid-November was accelerating into exponential growth they scrambled and adopted draconian measures to induce an inflection point, which they now claim to have reached. Every country that has had some success in combatting Covid-19 has adopted some version of that approach--introduce drastic measures to induce an inflection point that will break the exponential rate of increase and prevent a breakdown of the healthcare system. (For an account of the flaws in the Chinese response, see this very informative article from the SCMP: Coronavirus: China’s first confirmed Covid-19 case traced back to November 17.)

Thus the narrator concludes:

"If people are sufficiently worried, then there's a lot less to worry about. But if no one is worried, that's when you should worry."

Keep those words in mind when assessing our own government's response.


  1. Take a look at what Heather MacDonald writes in The New Criterion:

    I'm all for caution. But my sense, as we race through this, is we are living atop a media induced panic. We'll get to know the truth in a few weeks, I hope, about the lethality of this virus, which we CAN'T know now because we don't know how many people actually have it, or have already had it. The models the extrapolators are using are like any model, hostage to assumpations.

    The more I read, the more I think we would have been better off segregating at risk folks, people living in nursing homes, other elderly, the sick.

    Everybody isn't at risk for this.

    You have to watch Zero Hedge. Lots of dingbats over there. The beauty of the whole thing is if exponential growth in cases doesn't happen, the powers that be can say, "We saved you!" I don't see how we would know if they were wrong. How would you test for it?

    So, put me down for overreaction.

    This may be the rare time I somewhat disagree with you. Your blog is an absolute go to place. You are reasonable, dispassionate, given to in-depth, detailed analysis of important political events. And you damn well may be right here. I respect your views.

    I may be completely wrong. And if I'm wrong, people could die. So you have the precautionary principle going for you. Sidebar: Trump looks like hell.

    He's finally up against something he can't beat with his energy and tenacity and optimism. For the first time in his life, it's lose-lose. He kills the economy, or (worst case) people die, and he takes the blame.

    1. I can't claim I'm right, but here's what I'm reasoning from:

      The reaction of governments pretty much around the world.

      The Chinese government pretty much trashed their economy to get this under control. I don't believe the Chicoms did that because they love their subjects. I believe they did it because they feared the consequences of letting it continue. That wasn't a media induced panic--the government there controls the media.

      Italy and Iran, which have reacted slowly, have paid the consequences in a healthcare meltdown. That's fact. I have to assume that governments are getting the best possible medical and epidemiological advice before they take such drastic measures.

      The claim that young people are not at risk is a misinterpretation of the data:
      It's quite true that older people have a VERY high mortality rate. But the mortality for the youngest groups @ .2% is still around twice what is typical for flu. That should not offer any comfort.

      This virus has been confirmed to be more transmissible than other viruses and the fact that it has spread around the globe so quickly is almost certainly further confirmation of that. The higher the number infected, the greater the risk of more mortalities--irregardless of the rate.

      I read MacDonald. She doesn't actually address a single one of those facts.