The BFP (Benford-Fibonacci-Perez) method validates the consistency of COVID-19 epidemiological data in France and Italy

The Benford method can be used to detect manipulation of epidemiological or trial data during the validation of new drugs. We extend here the Benford method after having detected particular properties for the Fibonacci values 1, 2, 3, 5 and 8 of the first decimal of 10 runs of official epidemiological data published in France and Italy (positive cases, intensive care, and deaths) for the periods of March 1 to May 30, 2020 and 2021, each with 91 raw data. This new method – called “BFP” for Benford-Fibonacci-Perez - is positive in all 10 cases (i.e. 910 values) with an average of favorable cases close to 80%, which, in our opinion, would validate the reliability of these basic data.


Introduction
On the one hand, there is Benford's law ( http://www.fusioninvesting.com/2009/11/benfords-law-and-fibonacci-numbers/ ) which stipulates that the majority of series of measurements more or less linked to natural or biological phenomena are confirmed, if they are now, to this law which is defined as follows: In ( http://www.fusioninvesting.com/2009/11/benfords-law-and-fibonacci-numbers/ ) we note: « Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty. This counter-intuitive result has been found to apply to a wide variety of data sets, like electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and biological (which are very common in nature). It is named after physicist Franck Benford,who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881. Particularly, in epidemiology and health drugs trials, this law permets to validate accuracy and réalité of basic data ». This can therefore help detect fraud in scientific publications as well as unintentional errors in these datasets.
Often, we present the Fibonacci sequence as an example of a distribution obeying my Benford law fairly well.
On the other hand, there is, precisely, this Fibonacci law: Well known in natural forms: nautilus spiral, sunflower flowers, pineapple, palm trees or pine cones, Fibonacci numbers also control the relative proportions of TCAG nucleotides in DNA: we had already demonstrated this 30 years ago ( Perez, 1991), (Perez, 1997).
More recently, we have shown that these same Fibonacci proportions of the genome of the mitochondria, the energy source of the human cell, are deteriorated by mutations associated with various cancers (perez, 2017). We also demonstrate how these same Fibonacci proportions of DNA make it possible to distinguish a genome of a real bacterium from its attempt at a synthetic chimera (Perez, 2019).
In the field of SARS-CoV2, its mRNA vaccines, and its multiple variants, we have demonstrated since the start of the COVID-19 pandemic how these Fibonacci numbers offered a new angle for the analysis of mRNA sequences and mutations of SARS-CoV2: a biomathematic point of view of the genome , , mRNA vaccines or variants (Perez, 2021a), or the last Indian variant "Delta" B.1.617.2 (Perez , 2021b).
The paradox which is at the source of our method: On the one hand, Benford's law is often illustrated by its "good correlation" when applied to the Fibonacci sequence, which everyone knows is at the root of many forms of nature.
On the other hand, when we observe this same histogram, taken as proof of Benford's law by the primes, I note, on the contrary, that the (Fibonacci) numbers 1 2 3 5 and 8 differ in this histogram other numbers 4 6 7 and 9 (see Figures 2 § 3, and Table 1).
It is this observation which will be at the root of our method, then illustrated by this article.   What about the "BFP" method running on the firsts Fibonacci numbers? It seems that our "BFP" law is all the more clear that the Fibonacci numbers are small here 27 on the first 34 = 79.41%. For any whole number in the list, consider only its decimal with the highest weight decimal.

Methods and datas
Example: 13 ==> 1 3398 ===> 3 4765 ===> 4 If the selected decimal digit belongs to fibonacci 1 2 3 5 8 do +1 Otherwise 4 6 7 9 0 do +0 We then calculate the% of positives / total.   Here is the expected result on the public data covid19 in France and in Italy between March 1 and May 30 in 2020 and in 2021. Then, having the RELIABILITY of these basic data, we will illustrate an example of application: bravais correlations pearson in France (data smoothed over 7 sliding days) on time between positive test and death. The results obtained here, that is to say nearly 80% success for 910 real values cumulating 10 races of 91 values each coming from epidemiological measurements in France and Italy, are they GREATER than what would be produced by CHANCE? To answer this question, we performed 100 random batches, each simulating 910 representative random values, for a total of 91,000 random tests. Here are the results: While the number of successes of real cases is 725 favorable cases (first significant number = 1,2,3,5 or 8), the 100 batches produce an average number of successes of 667.96 with random values between 641 and 697 ( Figure 4).

Conclusions
Benford's law already makes it possible to validate or doubt the relevance, reliability and non-manipulation of batches of natural or medical data. What we are proposing today is beyond this Benford law, it is a PARTITION of the first 9 digits (or 10 when, as here, there is also some null data) in 2 clusters: Fibonacci cluster (1 2 3 5 8) and non-Fibonacci cluster (0 4 6 7 9). We suggest that the Fibonacci numbers cluster are all the more in the majority the more the data set is reliable and real. This constitutes a breakthrough in the analysis of natural, social and medical data. This method and the prospects that it should now be consolidated and deepened.
Finally, we have demonstrated by 91,000 random values draws that the "BFP" law applied to the 910 COVID-19 epidemiological values of France and Italy studied here produces results which cannot result from mere chance.