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Thurner et al. largely solve an imaginary, nonexistent problem. The curves they are looking at are the summed, cumulative ones. Depending on the stage in the development even the slope itself is hard to make out, far less its curvature. In all the curves of infection rate I've seen so far there always were exponential sections with discernible breaks at points of regime change. Of course the sum of differing regional trends may spread those breaks and seem nearly linear over all.
Fetaya et al. looks in danger of becoming one more source for the prevalent cases of circular reasoning in the humanities. Taking a single, individual text it may well be possible to reconstruct missing parts with some confidence. But those reconstructions will then be similar to (proto-)typical examples of their genre. You'll hardly ever learn anything new this way. The danger lies in adding these reconstructions to the corpus of known texts and basing future guesses and putative readings on them.
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