For daily case report data considered here t = 1, which is shorter than the serial interval of influenza. Using only the previous day's data (t = 1), as outlined above, results in slow convergence of the method since changes in the case numbers are due mostly to the case numbers more than t days earlier. Faster convergence and tighter bounds on R are obtained if R is calculated using a weighted sum of L and M stretching back in time beyond the serial interval. The weighting used is the temporal distribution of the serial interval, taken to be gamma distributed here, which weights earlier days relative to how likely the serial interval was to be that long. See below for further discussion on the serial intervals used in the analysis.