Mister Node is happy. He has spent quite some time to understand what is going on with COVID-19 in six jurisdictions. He has found a structure, a tableau to show his findings. There is, of course, a problem. It is too much information and too complicated. So these are useless to reach the COVID deniers. I show for a beginning, Node thought, the tableau for a simple and small jurisdiction like the Netherlands, in Fig. 1. It covers 29 weeks, from December 29, 2019 to July 17, 2020. But it is too difficult and he recommends readers look at it diagonally for the time being and to read the few tips below that make everything simpler.
The tableau is about the Netherlands.
Graph 1 in Fig. 1 (top left) illustrates when effective measures were first taken. That is in week 14, when the standard forecast for the growth in the number of COVID deaths (the model) will deviate systematically upwards from the empirical observations, after a period of tallying (and roughly being equal) over several weeks. That point is found by starting the model in week 9 at a reproduction number of 2.65. This method identifies the first week with effective measures. To the left of the line with the model is the line of observed infections (which precedes fatalities), and to the right of the model is the line of COVID deaths as observed (which numbers are lower than the numbers of the model that gives those as expected without measures.)
Aside from recognizing what the lines represent, there are a few tricks to read the charts from the tableaux. But first, the meaning of the lines used must be fully defined. They are in line with how we understand the pandemic with our common sense. Mister Node gives them (the lines) a letter that indicates their meaning:
- I for all infected people registered up to the corresponding week
- S (m) for the number of sick people at the moment (model-based, red)
- D (m) for all deaths expected without measures at the moment (model-based)
- R (m) for all recovered until then (model-based, red)
- D (o) for all deaths registered (these 5 are shown in graphs 1 and 2)
- NI the number of newly registered infected persons (graph 3) and
- ND the number of new deaths recorded (Graph 4)
The example from fig. 1 is the tableau, as instantiated for the Netherlands. Elsewhere the other tables follow (for China or the PRC, the USA, the UK, France and Brazil.) Each tableau has four graphs. These are the graphs that Mr. Node works with to keep the images for the different jurisdictions comparable. They seek and find a foothold in reality through the registered infections I and fatalities D (o) that he derives from Worldometers. For reading he tableaus one also needs to be able to read the movements that the lines indicate. Here follow a few tricks. Recognizing the meanings of a few curved and straight shapes suffices.
Lines follow the time in weeks (so the movement is always from left to right). If a curve is formed over a period of several weeks, it concerns exponential growth (the left curve), a tipping point (the middle one) or exponential decrease (the right curve). Unlike straight lines (which are suitable for extrapolation), exponential growth is getting out of hand at a pace that is not expected by many, nor is it considered plausible, so it is difficult to predict without conscious calculations. An example: with an unrestrained reproduction number of 2.65, the number of deaths in the Netherlands would have included the entire population in week 24, the week of June 12, more than a month before this piece was written. This does not mean that the model is no good. It means that no effective measures had yet been taken prior to week 14, the effect of which became visible in the development of the number of deaths. Because during the first five weeks of the epidemic in the Netherlands, it did develop along the aforementioned line. It therefore means that effective measures were taken in week 14. Apparently, such measures were taken in week 13 (the week of March 27) or shortly before (and yes). This gives us a simple rule of thumb: as long as a line has a curvature, there is exponential growth or decrease (or a tipping point), the consequences of which elude our common sense. An upward curve is a reason for near panic and action. The other forms are reasons for optimism.
As soon as there is a straight line (an arrow), the world becomes predictable for us because that is the way we are used to extrapolate our observations or, in other words, to look to the future with our common sense. Up means growth, horizontal means standstill, down means decrease.
The two sets (curves and arrows) have coherent but non-identical meanings for two different line types. For lines that indicate numbers per week (as NI, ND and S (m)), the meanings are as outlined. For the lines that indicate totals (as I, D (m), D (o) and R (m)), the downward movements do not occur because such lines can never give lower numbers than previous values. When these lines are horizontal they indicate that no more newly infected, sick, dead or recovered have occurred (while at the same time showing the total numbers).
To create the tableaux, Node needed data and decided to focus on developing mortality rates because he expected the numbers to be incomplete anyway, also because the pandemic was something new at its outset, while the numbers on COVID fatalities would be the most reliable. He also distinguished two phases for his analysis: the first one of being unprepared and cought off guard and in which no measures have yet been taken, and the second of adaptation and designing and refitting and promulgating measures. To determine when a policy was deployed with measurable effects on the observed number of fatalities, he used (as mentioned) a contamination curve characterized by a reproduction number per week. To be continued …
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