Align cumulative Hill model with latest data

[eschrom]

A Hill model fit directly on cumulative uptake does not account for seasonal variation - it only finds the "average" uptake S curve. So for any specific season, in-season projections do not pick up right where the data left off. This must be corrected. Below is an idea from @swo:

Or, maybe, the model should be looking at cumulative uptake after the last observed data point? Like, if you observe cumulative u t up > to timepoint t ⋆ , and the cumulative uptake is a function f ( t ) , then your projections are u ( t ⋆ ) + [ f ( t ) − f ( t ⋆ ) ] or something