> Note that excess is not defined as a deviation from a typical year, but as a deviation from a typical year when no diseases are circulating.
Data is deseasonalized, which does not mean what you wrote.
You are correct that I oversimplified a complex situation. https://euromomo.eu/how-it-works/methods/ describes their method, especially section "Hypothesis".
Their model includes a sinusoidal seasonal component, as you noted. However, what I said is also true. From the Hypothesis section, third bullet:
"Parts of Spring and Autumn are less likely to be influenced by additional processes leading to excess deaths and the main pattern of mortality can therefore be modelling using only those periods, resulting in a baseline being the number of deaths expected when no particular process increases mortality."
As is clear from the bullet that precedes the text that I quoted, "processes leading to excess deaths" means winter infections and summer heat waves. So my description, while incomplete, is hopefully not too misleading. For completeness, I should mention that they also adjust for population growth. (You can't just do 2020-avg(2015-2019) because the total population is different.)
Stepping back from the details for a minute: this is a 15-year long joint effort of public health authorities in Europe, with the explicit goal "to design a routine public health mortality monitoring system aimed at detecting and measuring, on a real-time basis, excess number of deaths related to influenza and other possible public health threats across participating European Countries." In terms of data analysis, their model is very simple, comprising a constant, a linear trend term for population growth, and a sine-wave term for non-flu seasonality. Do you really think that they would be so incompetent as to use a model that explicitly removes the flu, which is the very effect that they are trying to capture? Give them some credit, they know what they are doing.