The reason why the original logistic equation suffers in its predictive power is that it assumes that the exponential growth coefficient includes an asymptotic limiting factor incorporating an effective population "carrying capacity" or "herd immunity", but that this must be known *a prior* to the process's initiation. In other words, how would the initial dynamics of an epidemic's growth know anything about the ultimate carrying capacity? It can't and because of this conflation between growth and decline in the logistic equation's formulation, it makes no sense to apply it over the entire time interval. An alternative formulation is needed that separates the growth dynamics from the carrying capacity and this is the context of how a more general dispersive growth model is derived.
For the virus contagion, the "flattening of the growth curve" is important as one can see in the China situation, growth initially exploded but it nowhere near reached the potential offered by China's total population. More info is needed to understand the limiting factor in the contagion.