One should never differentiate a sampled signal without a low-pass filter (at least second order is preferred). The original cases/day plot was smooth, but also leveled off at the end. IDK if the people collecting the data are on any kind of weekly schedule, but that type of thing would certainly come through in the data with enough samples and Fourier analysis.
[0]http://en.wikipedia.org/wiki/File:Deseased_per_day_Ebola_201...