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Calibration per jurisdiction: scale matters

We started by showing a graph of how the pandemic developed numerically in the world by showing the model’s infection numbers and the observed infection numbers together. That led to Fig 1.

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Fig. 1

Fig. 1 illustrates the world data (see top left) that have been modified in three ways to allow comparison. The rough data would look like in Fig. 2. The red line from figure 2 has been shifted to end up as shown in fig. 1. The model can be shifted in time, but the observations cannot. This form of calibration respects the fact that the model of algorithm0 may have started operating in different jurisdictions at different times. The model assumes that COVID-19 appeared in the world on December 29. The observation shows that if the model is a bit correct, the first infection must have been one week earlier. In the middle of the bar to the right of the figure is a slide that allows the image to be calibrated in this respect. It’s called root-shft. It stands at -1, which means that the model comes into action one week earlier than originally planned. Which seems to correspond to what has been published about the start of the pandemic since March 19 (when I made the model).

But there is another important difference between the rough representation in Fig. 2 and the calibrated model. The reproduction number R-zero has also been adjusted (from 2 to 1.78) using the top center slider. This form of calibration deserves (and receives) separate treatment.

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Fig. 2

There is one more point to be made here that can be further elucidated with Fig. 3: it’s about choosing the scale.

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Fig. 3

In FIG. 3, the model has been associated with the figures for the Netherlands. The Netherlands has 17 million inhabitants and the model exceeds that number in the week after the week starting on day 133. When we try to display the model for such numbers, the differences of the period in question become invisible. Scale matters, as the rough picture in Fig. 4 shows.

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Fig. 4

We can now also show what happens if we want to calibrate the model to the observed data for the Netherlands in fig. 5:

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Fig. 5

Like the vertical line in Fig. 1, the one in Fig. 5 indicates at what point in time the model of algorithm 0 will deviate unacceptably from the observed data. In FIG. 1 is at day 98, in FIG. 5 at day 105.

It is noteworthy that, in order to obtain this result, the model had to be calibrated in such a way that it entered into force for the Netherlands seven weeks later than for the world. Whether this means anything and if so what needs further consideration.