You can assume that as long as you're far below saturation. Yes, the logistic curve comes to play at some point, slowing down the spread, stopping at some large

You can assume that as long as you're far below saturation. Yes, the logistic curve comes to play at some point, slowing down the spread, stopping at some large proportion of the population - it's plausible that two thirds of Americans will be infected, but that will take longer. However, until the total number of infected is less than, say, 10% of total population, it certainly makes sense to just use the average doubling rate.