Ordinary Differential Equation model, Partial Differential Equation model, Finite Difference model, etc.
Science worked fine. Politics did not. This is not specific to Germany.
That is simply not true. The RKI (Germany's main institute for disease control and prevention) almost exactly predicted the current Covid numbers back in July [1]. The top left of the picture on page 7 shows the prediction under the assumption that 65% of Germans get vaccinated; currently 68% of Germans are vaccinated.
[1]: https://www.rki.de/DE/Content/Infekt/EpidBull/Archiv/2021/Au...
The prediction expected a bell curve peaking at the end of December, at around 400 7d incidence, assuming ~65% vaccinated.
We are at then end of november, ~68% vaccinated, and the 7d incidence is already above 400, and still rising.
We can only hope that they got the shape right, the timing slighly off and the peek not too off.
I personally think that for such a chaotic, human system, a prediction from six-months previous is pretty good if it's within a few weeks and probably less than an order of magnitude.
I actually never expected that somehow my home country would be able to manage better at decisions, instead of the yes/no/but-elections-are-coming that we had here.
Corona brings live and death questions to the doors of normal people and also plays havoc with our political parties. It is embarrasing to observe to watch them for the most part. Seems for some of them the first problem they really have to work on instead of only talking about it.