5 ms·

there really can't be an "exponential" increase in the number of cases, whatever that means, given that there's a hard upper bound which is the number of hosts.

stnmtn 5y ago
While technically correct, you and I both know what they meant by exponential. Sure, there's a limit, but if we're looking at function that is exponential until it reaches an inflection point where there's simply less hosts to infect than possible...
- rolph 5y ago
  a rate of change in the rate of change, to wit a second order derivative
- oneoff786 5y ago
  By exponential, you mean there’s a steep part but you don’t really know the difference between exponential and logarithmic. The rapid slowdown of infections is FAR below 100% of people.
  - stnmtn 5y ago
    > Sure, there's a limit, but if we're looking at function that is exponential until it reaches an inflection point where there's simply less hosts to infect than possible... What do you think I meant by this? Do you think I believe that the rate of infection will keep going up literally exponentially until it hits 7 billion then turn flat, or do you think that by my usage of 'inflection point' maybe I had more nuance than that?
    - oneoff786 5y ago
      I took it to mean you’re claiming growth is exponential or nearly exponential until it nears 100% like a sigmoid function. But that’s wrong. Growth stalls out much much earlier. It’s just not right to call disease spread exponential.
      - stnmtn 5y ago
        In a math classroom, you are right. But when we're in a context of talking about the disease on an internet forum, you are being needlessly pedantic and extremely nitpick-y if you expect people to describe the ways infections grows as "similar to a sigmoid function" rathan than the well-understood and extremely common "exponential growth" term.
        oneoff786 5y ago
        I don’t really care if you say sigmoid when you mean exponential, my point is that both of those are wrong. People shudder in fear of the phrase “exponential” but disease does not spread exponentially. It never does. That’s a laymen fairy tail and it does a great deal of harm in understanding the disease. Exponential is not well understood. People don’t know what it means, as evidenced by the fact that they consistently use it incorrectly.
        renaudg 5y ago
        >disease does not spread exponentially. It never does. That’s a laymen fairy tail and it does a great deal of harm in understanding the disease. >Exponential is not well understood. People don’t know what it means, as evidenced by the fact that they consistently use it incorrectly. Well, in typical Dunning-Krüger fashion you're lecturing us laymen about the wrong use of "exponential", but it seems that you are the layman when it comes to epidemiology modelling. Diseases of course spread in an initially exponential phase, not logarithmically as you boldly claim in another comment. Epidemiologists talk about exponential disease growth all the time, here's one example : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6962332/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6962332/
        refytedy 5y ago
        Not the original commenter and agree with your sentiment. That said, from what we know about random graph models, once the transmission rate passes a certain threshold, the cumulative number of eventually infected individuals will NOT scale exponentially as the transmission rate increases. You're speaking about initial growth rate though, not convergent size of the once-infected population, which is definitely exponential and relevant if you care about minimizing simultaneous hospitalizations.
- erik_seaberg 5y ago
  That is the https://en.wikipedia.org/wiki/Logistic_function https://en.wikipedia.org/wiki/Logistic_function, which is pretty close to exponential growth followed by logarithmic saturation.
renaudg 5y ago
Look, no need to be pedantic about this : the only thing that counts here is whether it's still in the initial exponential phase by the time we hit maximum hospital capacity. It seems likely.

stnmtn 5y ago

While technically correct, you and I both know what they meant by exponential. Sure, there's a limit, but if we're looking at function that is exponential until it reaches an inflection point where there's simply less hosts to infect than possible...

rolph 5y ago
a rate of change in the rate of change, to wit a second order derivative
oneoff786 5y ago
By exponential, you mean there’s a steep part but you don’t really know the difference between exponential and logarithmic. The rapid slowdown of infections is FAR below 100% of people.
- stnmtn 5y ago
  > Sure, there's a limit, but if we're looking at function that is exponential until it reaches an inflection point where there's simply less hosts to infect than possible... What do you think I meant by this? Do you think I believe that the rate of infection will keep going up literally exponentially until it hits 7 billion then turn flat, or do you think that by my usage of 'inflection point' maybe I had more nuance than that?
  - oneoff786 5y ago
    I took it to mean you’re claiming growth is exponential or nearly exponential until it nears 100% like a sigmoid function. But that’s wrong. Growth stalls out much much earlier. It’s just not right to call disease spread exponential.
    - stnmtn 5y ago
      In a math classroom, you are right. But when we're in a context of talking about the disease on an internet forum, you are being needlessly pedantic and extremely nitpick-y if you expect people to describe the ways infections grows as "similar to a sigmoid function" rathan than the well-understood and extremely common "exponential growth" term.
      - oneoff786 5y ago
        I don’t really care if you say sigmoid when you mean exponential, my point is that both of those are wrong. People shudder in fear of the phrase “exponential” but disease does not spread exponentially. It never does. That’s a laymen fairy tail and it does a great deal of harm in understanding the disease. Exponential is not well understood. People don’t know what it means, as evidenced by the fact that they consistently use it incorrectly.
        renaudg 5y ago
        >disease does not spread exponentially. It never does. That’s a laymen fairy tail and it does a great deal of harm in understanding the disease. >Exponential is not well understood. People don’t know what it means, as evidenced by the fact that they consistently use it incorrectly. Well, in typical Dunning-Krüger fashion you're lecturing us laymen about the wrong use of "exponential", but it seems that you are the layman when it comes to epidemiology modelling. Diseases of course spread in an initially exponential phase, not logarithmically as you boldly claim in another comment. Epidemiologists talk about exponential disease growth all the time, here's one example : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6962332/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6962332/
        refytedy 5y ago
        Not the original commenter and agree with your sentiment. That said, from what we know about random graph models, once the transmission rate passes a certain threshold, the cumulative number of eventually infected individuals will NOT scale exponentially as the transmission rate increases. You're speaking about initial growth rate though, not convergent size of the once-infected population, which is definitely exponential and relevant if you care about minimizing simultaneous hospitalizations.
erik_seaberg 5y ago
That is the https://en.wikipedia.org/wiki/Logistic_function https://en.wikipedia.org/wiki/Logistic_function, which is pretty close to exponential growth followed by logarithmic saturation.

renaudg 5y ago

Look, no need to be pedantic about this : the only thing that counts here is whether it's still in the initial exponential phase by the time we hit maximum hospital capacity. It seems likely.