Figure ... : https://0x0.st/i9C7.png Due to covariance with scale parameters it is difficult or impossible to meaningfully fit exponential rise. If you fix the shape, you can estimate duration, or vice versa. In a worst case scenario, the model gains predictive power after the peak, as is shown by comparison of two SIR curves in the figure above. A major problem we could be seeing now is whether or not the distribution has a plateau. If it has a plateau, then the naive SIR is pretty much out the window, along with its particular parameters. Trying to fit SIR during a plateau is not a good idea. --Brad