# A Bayesian Analysis of the Inversion of the SARS-COV-2 Case Rate in the Countries of the 2020 European Football Championship

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection

#### 2.2. Bayesian Changepoint Detection and Analysis

## 3. Results

#### 3.1. Countries That Participated in the Tournament

#### 3.2. Countries That Did Not Participate in the Tournament

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Inversion of the SARS-COV-2 case trend for Austria, Belgium, Croatia, Czechia, Denmark, Finland. France, Germany, Hungary, and Italy, occurring not later than 2–3 weeks after their first match. Yellow space: duration of the tournament. Red vertical line: first match. Purple vertical line: last match. Green vertical line: last hosted match. Blue vertical line: changepoint. Blue space: CI amplitude for the changepoint. Blue bell-shaped peaks: peaks of the probability density function for the changepoint. Green segment: case rate trend before the changepoint. Red segment: case rate trend after the changepoint. Grey segments: fitted lines drawn randomly from the posterior distribution, based on the corresponding CI. Black dots: number of daily CARS-COV-2 cases. Rightmost y axis: number of cases. Leftmost y axis: logarithm of the number of cases.

**Figure 2.**Inversion of the SARS-COV-2 case trend for the Netherlands, North Macedonia, Poland, Slovakia, Spain, Switzerland, and Ukraine, occurring not later than 2–3 weeks after their first match. Yellow space: duration of the tournament. Red vertical line: first match. Purple vertical line: last match. Green vertical line: last hosted match. Blue vertical line: changepoint. Blue space: CI amplitude for the changepoint. Blue bell-shaped peaks: peaks of the probability density function for the changepoint. Green segment: case rate trend before the changepoint. Red segment: case rate trend after the changepoint. Grey segments: fitted lines drawn randomly from the posterior distribution, based on the corresponding CI. Black dots: number of daily CARS-COV-2 cases. Rightmost y axis: number of cases. Leftmost y axis: logarithm of the number of cases.

**Figure 3.**Portugal, Russia, Sweden, Turkey, and the UK break the pattern, without: (i) a well-recognizable changepoint and (ii) a reversal from a decrease to an increase in the SARS-COV-2 case rate, occurring not later than 2–3 weeks after the beginning of the tournament. Yellow space: duration of the tournament. Red vertical line: first match. Purple vertical line: last match. Green vertical line: last hosted match. Blue vertical line: changepoint. Blue space: CI amplitude for the changepoint. Blue bell-shaped peaks: peaks of the probability density function for the changepoint. Green segment: case rate trend before the changepoint. Red segment: case rate trend after the changepoint. Grey segments: fitted lines drawn randomly from the posterior distribution, based on the corresponding CI. Black dots: number of daily CARS-COV-2 cases. Rightmost y axis: number of cases. Leftmost y axis: logarithm of the number of cases.

**Figure 4.**Azerbaijan, Bosnia, Bulgaria, Greece, Iceland, and Ireland not participating countries. Yellow space: duration of the tournament. Red vertical line: first match. Purple vertical line: last match. Green vertical line: last hosted match. Blue vertical line: changepoint. Blue space: CI amplitude for the changepoint. Green segment: case rate trend before the changepoint. Red segment: case rate trend after the changepoint. Blue bell-shaped peaks, grey segments, black dots, and rightmost and leftmost y axis: same as in previous figures.

**Figure 5.**Latvia, Lithuania, Moldova, Norway, Romania, and Serbia not participating countries. Yellow space: duration of the tournament. Red vertical line: first match. Purple vertical line: last match. Green vertical line: last hosted match. Blue vertical line: changepoint. Blue space: CI amplitude for the changepoint. Green segment: case rate trend before the changepoint. Red segment: case rate trend after the changepoint. Blue bell-shaped peaks, grey segments, black dots, and rightmost and leftmost y axis: same as in previous figures.

**Table 1.**Countries with a changepoint coincidental with a reversal from a decrease to an increase in the SARS-COV-2 case rate that occurred during the European football championship.

Country (Participating in the Tournament) | τ (Changepoint, avg. Value and 95% CI) | Diff (Days Separating τ from First Match) | b_{1}(Angular Coefficient before τ, avg. Value and 95% CI) | b_{2}(Angular Coefficient after τ, avg. Value and 95% CI) | a_{1}(Intercept before τ, avg. Value and 95% CI) |
---|---|---|---|---|---|

Austria | 36.4 (35.8, 37.1) | 20 | −0.05 (−0.06, −0.05) | 0.08 (0.08, 0.09) | 6.28 (6.25, 6.32) |

Belgium | 24.9 (24.6, 25.2) | 10 | −0.06 (−0.06, −0.06) | 0.04 (0.04, 0.04) | 7.70 (7.68, 7.71) |

Croatia | 28.7 (27.4, 30.3) | 13 | −0.06 (−0.06, −0.06) | 0.02 (0.02, 0.03) | 5.87 (5.83, 5.92) |

Czechia | 26.2 (25.3, 27.2) | 9 | −0.06 (−0.06, −0.05) | 0.02 (0.02, 0.03) | 6.30 (6.26, 6.34) |

Denmark | 28.2 (27.8, 28.6) | 13 | −0.06 (−0.06, −0.06) | 0.05 (0.05, 0.06) | 7.13 (7.11, 7.15) |

Finland | 19.8 (18.4, 21.0) | 5 | −0.03 (−0.04, −0.03) | 0.04 (0.04, 0.05) | 4.98 (4.90, 5.05) |

France | 34.7 (34.6, 34.8) | 17 | −0.06 (−0.06, −0.06) | 0.11 (0.11, 0.11) | 9.28 (9.28, 9.29) |

Germany | 35.1 (34.6, 35.5) | 17 | −0.07 (−0.07, −0.07) | 0.05 (0.05, 0.05) | 8.60 (8.59, 8.62) |

Hungary | 40.3 (38.4, 42.0) | 22 | −0.06 (−0.06, −0.06) | 0.03 (0.02, 0.05) | 5.99 (5.95, 6.03) |

Italy | 36.5 (36.3, 36.8) | 23 | −0.05 (−0.05, −0.05) | 0.09 (0.09, 0.10) | 8.25 (8.24, 8.26) |

Netherlands | 26.4 (26.2, 26.6) | 10 | −0.06 (−0.06, −0.06) | 0.09 (0.09, 0.09) | 8.18 (8.17, 8.20) |

N. Macedonia | 34.8 (31.9, 37.6) | 19 | −0.05 (−0.05, −0.04) | 0.05 (0.04, 0.07) | 3.59 (3.46, 3.72) |

Poland | 35.2 (33.5, 36.8) | 18 | −0.07 (−0.07, −0.07) | 0.01 (−0.00, 0.01) | 6.92 (6.89, 6.94) |

Slovakia | 39.4 (36.8, 42.1) | 22 | −0.05 (−0.05, −0.04) | 0.02 (0.00, 0.03) | 5.02 (4.96, 5.08) |

Spain | 24.9 (24.8, 25.0) | 8 | −0.01 (−0.01, −0.01) | 0.07 (0.06, 0.07) | 8.45 (8.44, 8.46) |

Switzerland | 32.9 (32.5, 33.5) | 18 | −0.07 (−0.07, −0.07) | 0.08 (0.08, 0.08) | 6.93 (6.91, 6.96) |

Ukraine | 25.8 (25.1, 26.5) | 10 | −0.05 (−0.05, −0.05) | 0.00 (0.00, 0.01) | 8.06 (8.04, 8.07) |

**Table 2.**Quantifying the inversion from a decrease to an increase in the SARS-COV-2 case rate for the countries of Table 1.

Country | Days Needed to Halve the Number of Cases (before τ) | Days Needed to Double the Number of Cases (after τ) |
---|---|---|

Austria | 12.69 | 8.18 |

Belgium | 11.05 | 17.60 |

Croatia | 11.77 | 28.32 |

Czechia | 12.05 | 28.22 |

Denmark | 11.49 | 12.71 |

Finland | 21.81 | 15.84 |

France | 11.86 | 6.32 |

Germany | 10.14 | 13.17 |

Hungary | 11.10 | 22.10 |

Italy | 13.56 | 7.43 |

Netherlands | 12.11 | 7.69 |

N. Maced. | 14.88 | 13.20 |

Poland | 9.67 | 92.80 |

Slovakia | 14.91 | 41.59 |

Spain | 103.50 | 10.62 |

Switzerland | 10.03 | 8.56 |

Ukraine | 14.43 | 159.00 |

Country (Participating in the Tournament) | τ (Changepoint, avg. Value and 95% CI) | Diff (Days Separating τ from First Match) | b_{1}(Angular Coefficient before τ, avg. Value and 95% CI) | b_{2}(Angular Coefficient after τ, avg. Value and 95% CI) | a_{1}(Intercept before τ, avg. Value and 95% CI) |
---|---|---|---|---|---|

Portugal | 26.4 (2.4, 47.7) | 8 | 0.03 (0.01, 0.05) | 0.08 (0.08, 0.09) | 6.28 (6.25, 6.32) |

Russia | 38.7 (38.4, 39.0) | 24 | 0.03 (−0.03, −0.03) | 0.00 (0.00, 0.00) | 8.91 (8.90, 8.91) |

Sweden | 26.9 (7.9, 45.8) | 10 | −0.04 (−0.05, −0.02) | 0.00 (−0.04, 0.05) | 7.26 (7.15, 7.36) |

Turkey | 43.4 (43.1, 43.6) | 29 | −0.01 (−0.01, −0.01) | 0.05 (0.05, 0.06) | 8.93 (8.92, 8.94) |

UK | 52.6 (27.8, 28.6) | 37 | 0.05 (0.05, −0.05) | −0.04 (−0.05, −0.04) | 7.99 (7.98, 7.99) |

Country (Participating in the Tournament) | τ (Changepoint, avg. Value and 95% CI) | Diff (Days Separating τ from Beginning of Tournament) | b_{1}(Angular Coefficient before τ, avg. Value and 95% CI) | b_{2}(Angular Coefficient after τ, avg. Value and 95% CI) | a_{1}(Intercept before τ, avg. Value and 95% CI) |
---|---|---|---|---|---|

Moldova | 9.63 (6.52, 12.52) | −4 | −0.06 (−0.10, −0.03) | 0.01 (0.01, 0.02) | 4.36 (4.21, 4.50) |

Norway | 16.56 (15.09, 17.98) | 3 | −0.05 (−0.06, −0.04) | −0.00 (−0.00, 0.00) | 6.03 (5.98, 6.07) |

Azerbaijan | 24.16 (23.00, 25.32) | 10 | −0.08 (−0.08, −0.07) | 0.06 (0.05, 0.06) | 5.47 (5.41, 5.54) |

Greece | 26.03 (25.77, 26.31) | 12 | −0.06 (−0.06, −0.06) | 0.07 (0.07, 0.07) | 7.53 (7.51, 7.55) |

Ireland | 31.58 (30.53, 32.68) | 18 | −0.01 (−0.01, −0.01) | 0.06 (0.05, 0.06) | 6.05 (6.01, 6.08) |

Serbia | 34.84 (33.49, 36.20) | 21 | −0.05 (−0.05, −0.04) | 0.05 (0.04, 0.06) | 5.83 (5.79, 5.87) |

Lithuania | 39.12 (38.17, 40.08) | 25 | −0.08 (−0.08, −0.08) | 0.09 (0.08, 0.10) | 6.42 (6.39, 6.45) |

Latvia | 45.07 (41.54, 48.44) | 31 | −0.05 (−0.05, −0.05) | 0.02 (−0.01, 0.05) | 5.91 (5.87, 5.94) |

Romania | 37.60 (35.21, 39.90) | 24 | −0.06 (−0.06, −0.06) | 0.04 (0.03, 0.05) | 5.77 (5.72, 5.82) |

Bosnia and Herzegovina | 38.61 (36.16, 40.76) | 25 | −0.06 (−0.06, −0.05) | 0.04 (0.02, 0.06) | 4.63 (4.55, 4.70) |

Bulgaria | 39.82 (32.97, 44.20) | 26 | −0.04 (−0.04, −0.03) | 0.04 (0.01, 0.06) | 5.49 (5.44, 5.55) |

Iceland | 46.82 (44.85, 48.43) | 33 | −0.01 (−0.02, 0.00) | 0.31 (0.27, 0.36) | 1.40 (1.11, 1.70) |

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**MDPI and ACS Style**

Casini, L.; Roccetti, M. A Bayesian Analysis of the Inversion of the SARS-COV-2 Case Rate in the Countries of the 2020 European Football Championship. *Future Internet* **2021**, *13*, 212.
https://doi.org/10.3390/fi13080212

**AMA Style**

Casini L, Roccetti M. A Bayesian Analysis of the Inversion of the SARS-COV-2 Case Rate in the Countries of the 2020 European Football Championship. *Future Internet*. 2021; 13(8):212.
https://doi.org/10.3390/fi13080212

**Chicago/Turabian Style**

Casini, Luca, and Marco Roccetti. 2021. "A Bayesian Analysis of the Inversion of the SARS-COV-2 Case Rate in the Countries of the 2020 European Football Championship" *Future Internet* 13, no. 8: 212.
https://doi.org/10.3390/fi13080212