| There are different kinds of S-curves. Some of them are basically exponential at the beginning (the logistic curve). This makes perfect sense in modelling an infectious disease - initially, all contacts are susceptible. Thus you have exponential growth. Others, for example the CDF of a normal (which is often confused with the logistic), is not exponential at the beginning, but decays much faster (the derivative is exp(-x^2)). Arctan decays much slower (derivative is 1/(1+x^2)). So, S-curves are sort of linear in the middle, but sort of exponential or exp(-x^2) or 1/(1+x^2) or hyperbolic at the ends, and which one of them it is tells us a lot about their behaviour. Note also that without any social distancing or other measures and a sustained Rt of, say, 3, the inflection point will only occur once about a third of the population are infected, and thus it makes perfect sense to model it exponentially while still being below 5%, say. |