Infectious diseases rarely see actual exponential growth for logistical reasons. It's a pretty unrealistic model that ignores that the disease actually needs to find additional hosts to spread, the local availability of which starts to go down from the first victim.

If you assume the availability of hosts is local to the perimeter of the infected hosts, then the relative growth is limited to 2/R where R is the distance from patient 0 in 2 dimensions. It's becuase an area of the circle defines how many hosts are already ill but the interaction can only happen on the perimeter of the circle.

The disease is obviously also limited by the total amount of hosts, but I assume there's also the "bottom" limit - i.e. the resource consumption of already-infected hosts.

It also depends on how panicked people are. Covid was never going to spread like ebola, for instance: it was worse. Bad enough to harm and kill people, but not bad enough to scare them into self-enforced isolation and voluntary compliance with public health measures.

Back on the subject of AI, I think the flat part of the curve has always been in sight. Transformers can achieve human performance in some, even many respects, but they're like children who have to spend a million years in grade school to learn their multiplication tables. We will have to figure out why that is the case and how to improve upon it drastically before this stuff really starts to pay off. I'm sure we will but we'll be on a completely different S-shaped curve at that point.

Yes the model where the S curves comes out is extremely simplified. Looking at covid curves we could have well said it was parabolic, but that’s much less worrisome

It's obvious, but the problem was that enough people would die in the process for people to be worried. Similarly, if the current AI will be able to replace 99% of devs in 5-10 years (or even worse, most white collar jobs) and flatten out there without becoming a godlike AGI, it will still have enormous implications for the economy.