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...

That is the https://en.wikipedia.org/wiki/Logistic_function, which is pretty close to exponential growth followed by logarithmic saturation.

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.

> 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?

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.

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.

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.

>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/

A brief initial exponential phase that doesn’t explain the average state of the system is a poor mental model.

Epidemiologists do frequently use exponential growth in discussions of theoretical spreading, but they are not correct. It does not fucking matter. They’re just wrong. Is the long term spread of a disease exponential. No. We can say this with 100% confidence. Why? Because they do not increase exponentially over time. They QUICKLY hit ceilings and inflection points.

This is the problem. If you call a system exponential because it looks like that at the beginning, your estimates of the middle and end will be hugely off. Massively wrong.

It is obviously apparent looking at Covid that it does not spread exponentially. The impact of this understanding is enormous. In an exponential model, a virus that is twice as infectious could be expected to infect 4x as many people over the same period. If the model is logarithmic, twice as infectious will likely result in LESS THAN TWICE the number of people infected.

Scary predictions that a small increase in spreading will exponentially increase the number of infected people do not hold up against observed real world data. We should be cheering on a more spreadable but less deadly disease. Scale matters, of course, but we aren’t seeing anything like that.

If you want to come back to this in one year and check to see if omicron infected even twice the number of people that delta did over the same time period that’s a bet I’d surely take.

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.

a rate of change in the rate of change, to wit a second order derivative

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.