6 ms·

But the early stages of disease spread _are_ exponential. And I find that people really fail to understand the meaning of that, and how scary numbers like "new

But the early stages of disease spread _are_ exponential. And I find that people really fail to understand the meaning of that, and how scary numbers like "new confirmed cases doubling every two days, 500 new cases in France yesterday" truly are.

hef19898 7y ago
Yes, but extrapolating the early exponential phase is, plain and simple, mathematically wrong. No idea why data scientists aren't going the first mile and look up the relevant functions before spitting data out. Total fail on their part, IMHO.
- whatshisface 7y ago
  It's not wrong: it has produced extremely good predictive results day after day for total cases outside of China for months now. Using a simpler approximate function in place of a more complicated exact function is far from wrong, it is bread and butter for getting practical results in all areas of science.
  - zaroth 7y ago
    It’s right until it’s totally wrong, e.g. for any country which has already peaked, of which there are several.
    - goatlover 7y ago
      Countries that implemented extreme measures to slow the spread of the virus. It will be different for countries which haven't. The WHO and other health officials around the world are saying the same thing. This will spread to a large number of people. It's too late for containment, you can only hope to flatten the curve. That's why it's now a pandemic.
      - zaroth 7y ago
        > This will spread to a large number of people. It's too late for containment, you can only hope to flatten the curve. Follow the logic through. South Korea is detecting ~100 cases per day on top of a total of 7,700 and 66 deaths. Total population is 50 million people. How long do you shut down the economy over a disease where you are detecting 100 cases per day with a CFR of 0.8%? Seems like this is a perfect example of the curve being too flat.
        arpa 7y ago
        Unless you simultaneously ramp up your healthcare resources (what China did), even as "low" as 100 cases/day still has very real potential to go exponential (R0=2.5), overwhelm your healthcare, and kill 10% of our population if not more (especially if your population is aged).
        zaroth 7y ago
        I hear that, what I'm saying is, follow that logic through... If it's crucial to maintain strict protocols even during a rate of only 100 new cases/day, that means these protocols stay in place roughly... indefinitely. Counting individual cases and deaths in a country of 300 million is nonsensical. You could do the same thing with the flu and you'd hit 20,000 deaths a year and you'd destroy the economy in the process. IMO, the solution is best preparing to treat the number of people who do become severely ill from it, and getting the rest of the country fully back to work as quickly as possible. Although I disagree strongly on the "kill 10% of your population" bit, which is just fear-mongering, it's kind of besides the point.
        whatshisface 7y ago
        >Although I disagree strongly on the "kill 10% of your population" bit, which is just fear-mongering, it's kind of besides the point. If every case went untreated, 10% is a reasonable guess about what the death rate would be. Unchecked growth would lead to almost every case going untreated. That's the penalty for allowing the number of active cases to rise above five times the number of open beds/ventilators.
- Certhas 7y ago
  Mathematically wrong is not a relevant category here. There is no "ground truth" that is approximated by an exponential growth. Every disease model is counterfactual "spread of the disease if no countermeasures were taken", etc... Modelling the beginning of an epidemic as exponential growth is useful, sensible and empirically validated. As, countermeasures are taken during the beginning of the epidemic, for discussions of the effect of countermeasures, exponential is the correct model. In fact, hopefully the countermeasures taken will be sufficient that the intrinsic disease dynamic will never get past the exponential stage...
  - hef19898 7y ago
    I don't find any differentiation between early stage and later stage nor references to exponential functions: https://en.wikipedia.org/wiki/Mathematical_modelling_of_infectious_disease https://en.wikipedia.org/wiki/Mathematical_modelling_of_infe... If you find any source, idealy scientific papers on the subject, that shows that contagious diseases can be modelled with simple exponential functions, please share them. I am not an expert on that matter, so I would be really interessted to see some reliable sources confirming the use of exponential functions.
    - cvwright 7y ago
      Ok, look at the differential equations on this page about the Kermack-McKendrick model: https://mathworld.wolfram.com/Kermack-McKendrickModel.html https://mathworld.wolfram.com/Kermack-McKendrickModel.html Notice that the rate of change in the infected population (dI/dt) is proportional to the current number of infected (I) and the current number of susceptible (S). In the early stages, when S is large and I is still small, this acts just like an exponential function in I. For example, think about what happens when you double I the first several times. S stays relatively unchanged, and so dI/dt roughly doubles each time you double I. Does that make sense?
      - hef19898 7y ago
        Yeah, exactly. In the beginning exponential, later on not anymore. Without changing the equation. So, no, not exponential. Because, you know, very early on an exponential graph can approximated by something non-exponential. Would be utter BS, sure, so nobody does it.
ericol 7y ago
The problem is, exponential for how long? For instance, all seems to indicate measures in Italy are taken too late: and the exponential growth is still happening there (almost 3 weeks after the problem started) import pandas as pd import numpy as np import matplotlib.pyplot as plt %matplotlib inline it = pd.read_json('https://raw.githubusercontent.com/pcm-dpc/COVID-19/master/dati-json/dpc-covid19-ita-andamento-nazionale.json', convert_dates=True).set_index('data') plt.plot(it[['deceduti', 'totale_casi']]) plt.xticks(it.index.values, rotation=90);
- Certhas 7y ago
  It's to early to say. The people who are popping up with symptoms now might have been infected up to two weeks ago. If you look at the Wuhan data, you see that the lockdown worked, but the number of confirmed cases at the time continued to rise dramatically until 12 days after the lockdown went into effect. We are only three days in on the Italy lockdown. https://jamanetwork.com/journals/jama/fullarticle/2762130 https://jamanetwork.com/journals/jama/fullarticle/2762130 Figure 1.

hef19898 7y ago

Yes, but extrapolating the early exponential phase is, plain and simple, mathematically wrong. No idea why data scientists aren't going the first mile and look up the relevant functions before spitting data out. Total fail on their part, IMHO.

whatshisface 7y ago
It's not wrong: it has produced extremely good predictive results day after day for total cases outside of China for months now. Using a simpler approximate function in place of a more complicated exact function is far from wrong, it is bread and butter for getting practical results in all areas of science.
- zaroth 7y ago
  It’s right until it’s totally wrong, e.g. for any country which has already peaked, of which there are several.
  - goatlover 7y ago
    Countries that implemented extreme measures to slow the spread of the virus. It will be different for countries which haven't. The WHO and other health officials around the world are saying the same thing. This will spread to a large number of people. It's too late for containment, you can only hope to flatten the curve. That's why it's now a pandemic.
    - zaroth 7y ago
      > This will spread to a large number of people. It's too late for containment, you can only hope to flatten the curve. Follow the logic through. South Korea is detecting ~100 cases per day on top of a total of 7,700 and 66 deaths. Total population is 50 million people. How long do you shut down the economy over a disease where you are detecting 100 cases per day with a CFR of 0.8%? Seems like this is a perfect example of the curve being too flat.
      - arpa 7y ago
        Unless you simultaneously ramp up your healthcare resources (what China did), even as "low" as 100 cases/day still has very real potential to go exponential (R0=2.5), overwhelm your healthcare, and kill 10% of our population if not more (especially if your population is aged).
        zaroth 7y ago
        I hear that, what I'm saying is, follow that logic through... If it's crucial to maintain strict protocols even during a rate of only 100 new cases/day, that means these protocols stay in place roughly... indefinitely. Counting individual cases and deaths in a country of 300 million is nonsensical. You could do the same thing with the flu and you'd hit 20,000 deaths a year and you'd destroy the economy in the process. IMO, the solution is best preparing to treat the number of people who do become severely ill from it, and getting the rest of the country fully back to work as quickly as possible. Although I disagree strongly on the "kill 10% of your population" bit, which is just fear-mongering, it's kind of besides the point.
        whatshisface 7y ago
        >Although I disagree strongly on the "kill 10% of your population" bit, which is just fear-mongering, it's kind of besides the point. If every case went untreated, 10% is a reasonable guess about what the death rate would be. Unchecked growth would lead to almost every case going untreated. That's the penalty for allowing the number of active cases to rise above five times the number of open beds/ventilators.
Certhas 7y ago
Mathematically wrong is not a relevant category here. There is no "ground truth" that is approximated by an exponential growth. Every disease model is counterfactual "spread of the disease if no countermeasures were taken", etc... Modelling the beginning of an epidemic as exponential growth is useful, sensible and empirically validated. As, countermeasures are taken during the beginning of the epidemic, for discussions of the effect of countermeasures, exponential is the correct model. In fact, hopefully the countermeasures taken will be sufficient that the intrinsic disease dynamic will never get past the exponential stage...
- hef19898 7y ago
  I don't find any differentiation between early stage and later stage nor references to exponential functions: https://en.wikipedia.org/wiki/Mathematical_modelling_of_infectious_disease https://en.wikipedia.org/wiki/Mathematical_modelling_of_infe... If you find any source, idealy scientific papers on the subject, that shows that contagious diseases can be modelled with simple exponential functions, please share them. I am not an expert on that matter, so I would be really interessted to see some reliable sources confirming the use of exponential functions.
  - cvwright 7y ago
    Ok, look at the differential equations on this page about the Kermack-McKendrick model: https://mathworld.wolfram.com/Kermack-McKendrickModel.html https://mathworld.wolfram.com/Kermack-McKendrickModel.html Notice that the rate of change in the infected population (dI/dt) is proportional to the current number of infected (I) and the current number of susceptible (S). In the early stages, when S is large and I is still small, this acts just like an exponential function in I. For example, think about what happens when you double I the first several times. S stays relatively unchanged, and so dI/dt roughly doubles each time you double I. Does that make sense?
    - hef19898 7y ago
      Yeah, exactly. In the beginning exponential, later on not anymore. Without changing the equation. So, no, not exponential. Because, you know, very early on an exponential graph can approximated by something non-exponential. Would be utter BS, sure, so nobody does it.

ericol 7y ago

The problem is, exponential for how long? For instance, all seems to indicate measures in Italy are taken too late: and the exponential growth is still happening there (almost 3 weeks after the problem started) import pandas as pd import numpy as np import matplotlib.pyplot as plt %matplotlib inline it = pd.read_json('https://raw.githubusercontent.com/pcm-dpc/COVID-19/master/dati-json/dpc-covid19-ita-andamento-nazionale.json', convert_dates=True).set_index('data') plt.plot(it[['deceduti', 'totale_casi']]) plt.xticks(it.index.values, rotation=90);

Certhas 7y ago
It's to early to say. The people who are popping up with symptoms now might have been infected up to two weeks ago. If you look at the Wuhan data, you see that the lockdown worked, but the number of confirmed cases at the time continued to rise dramatically until 12 days after the lockdown went into effect. We are only three days in on the Italy lockdown. https://jamanetwork.com/journals/jama/fullarticle/2762130 https://jamanetwork.com/journals/jama/fullarticle/2762130 Figure 1.