["model"] Fitting to current census with a long projection can match to the down-slope

[PhilMiller]

Summary

Post #255 / #273 the model gets fit to the current hospitalized census. With a long forecast, the closest fitting day may be past the peak, when we actually want to fit to the closest pre-peak day.

Additional details

Suggested fix

Look for the peak in the range of predictions, and then compute minimum loss day among days up to that day.

[PhilMiller]

Playing with things a bit more, the prescribed-doubling-time mode is much more sensitive to this than the prescribed-first-hospitalization mode, because their fitting procedures differ.

[cjbayesian]

Very good catch, @PhilMiller. Indeed this is an issue with fitting days_since. It's finding the optimal solution on the other side of the curve, which makes perfect sense. Any way to keep it on the left side of the projection will fix this.

[cjbayesian]

If we create a row tracking DI/Dt then we can limit the search space to where this is > 0. As in, the slope of the infections curve has to be positive (eg on the left side of the hump).

[cjbayesian]

DI/Dt is precisely the admissions (scaled), so could just make use of that for the constraint.

[PhilMiller]

@cjbayesian I just noticed in your comments as I'm revisiting this - admissions is a rate coefficient times -dS/dt, not dI/dt - the latter term includes recoveries. This is exactly what you fixed in #189, a week prior.