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.