Earlier quoted context omitted.
> The steady state is exactly 1, which is like balancing a pencil on its point. At exactly one, it's indeterminate; you could see a subexponential growth or decay. With no exponential terms remaining, lower-order terms that are ordinarily hidden by exponential growth become the dominant observables. (Since epidemic spread is also random, you're much more likely to see the stochastic terms show up in the overall stati…
By the way, now that we are already talking about R ~= 1 ... Over pretty much the last year you could observe, in different countries all around the world, that the reproduction number was 'magically' floating around 1. Only recently did I learn that this effect was puzzling for epidemiologists as well and was only solved around 2012 (?) in a model that assumes a network of information about the disease in parallel t…
You can almost see the phenomenon in real time during this pandemic. Countries that have low trust in authorities will still freak out when the epidemic hits biblical proportions, and do various forms of impromptu distancing measures which will bring the R number down. Then when the signs of panic subside, they'll loosen them. And so on.
Societies with high trust in authorities will still pressure their authorities to loosen up when things feel safe, with predictible results, leading to further lockdowns.