My impression is that some Fermi estimate approaches assume that exponential growth indeed goes on until it hits the wall of 100%.
Exponential growth is represented by
ds/s = x, where s is the stock (here of infected people) and x is a constant.
To my intuition, logistic growth ds/s = y (1-s) is almost as simple and it has the feature of a built-in limit.
Of course both models imply 100% infection rates, but the second one asymptotically. The logistic model in this specification has highest absolute growth when 50% are infected, then lower (but still positive) growth because, e.g., infected people meet more who already infected.
My impression is that some Fermi estimate approaches assume that exponential growth indeed goes on until it hits the wall of 100%. Exponential growth is represented by ds/s = x, where s is the stock (here of infected people) and x is a constant. To my intuition, logistic growth ds/s = y (1-s) is almost as simple and it has the feature of a built-in limit. Of course both models imply 100% infection rates, but the second one asymptotically. The logistic model in this specification has highest absolute growth when 50% are infected, then lower (but still positive) growth because, e.g., infected people meet more who already infected.
Sorry if this is already common knowledge.