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I was surprised you didn't include a discussion of proportional change as opposed to absolute change here. Both types of change can be important. If you are looking to measure the human toll of the virus, the absolute change (e.g. 651 deaths in Italy yesterday) should reasonably be what you want to model most accurately - the difference between 10,000 and 12,000 is more important than the difference between 100 and 120. But if you want to understand the nature of the system, proportional change may be a more useful way of looking at the data. Due to the nature of disease spread, it is reasonable to conceptualize the system as one where exponential growth is expected, and deviation from that exponential growth might reasonably be interpreted as something meaningful - mode/observation mismatch of 20% is similarly important, whether that's 100 v.s 120, or 10,000 vs. 12,000.

BH: In the last part, you anticipated a post that currently sits in my head. It will probably appear this week or next. When there is a discrepancy between a model and the observed data, the modeler has to make a judgment call: how much of the gap is due to a mis-specified model and how much of it is due to poorly measured data? It can be some of each. Nevertheless, it's important to recognize that the exponential curve is an analytical solution to a theoretical setup so there is some basis for it to be "true".

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