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.
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.
Exponential growth. It's the growth phase that matters.
People keep mentioning the exponential because both of these curves, at an important point in time, grow very fast. Much faster than anything you're likely to encounter in daily life, so the public really doesn't have the requisite intuition.
But I can see you're not interested in understanding the point. You asked for equations, I gave you equations. Good day sir.
We are, I think, not disagreeing at all. May sound crazy, but bear with me a second here. I know that the initial phase of any epidemic is exponential. Key are these three small words, initial growth phase. Because they make all the difference, as every epidemic will ultimately peak.
These three words are simply to often drowned out in discussions about COVID-19. That's we you see extrapolations of this growth against, for example, the population of Italy. And this is dangerous. And I don't think we disagree here, I never disputed the exponential nature of the early phase.
We just shouldn't make the mistake in assuming everybody catches these three little words, especially not online.
The most critical question everybody is trying to answer right now is, when the peak will be. And whether this peak will to high for our medical infrastructure. With all the measures being taken, the conclusion seems to be the point will be too high. Hence the counter measures. So we should all do what we can to flatten the curve as much as possible. I never said anything else, and honestly, I don't see where are disagreeing here.
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?