One thing to note (from looking at the graph) is that the noise seems to be additive with constant standard deviation (and presumably floored floored such that

One thing to note (from looking at the graph) is that the noise seems to be additive with constant standard deviation (and presumably floored floored such that the sum doesn’t go negative). That means that there is huge relative error initially (we have 10 infections +/- 100), and very little relative error eventually (we have 1000000 infections +/- 100). I assume the forecasts would be better if the error were multiplicative (in other words, with standard deviation proportional to the current value). However, I think the main point stands: the forecasts get much better once one approaches the inflection point.