# Fuzzy Clustering Methods to Identify the Epidemiological Situation and Its Changes in European Countries during COVID-19

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

- COVID-19 cases per 100,000 population (x
_{1}), - COVID-19 deaths per 100,000 population (x
_{2}), - share of COVID-19 deaths in COVID-19 cases (%) (x
_{3}), - active cases—cumulative number for 14 days of COVID-19 cases per 100,000 (x
_{4}).

_{2}COVID-19 deaths per 100,000 population, in which the average diversity of values of this variable in European countries was 339.94%. In European countries, the coefficient of variation of the x

_{1}COVID-19 cases per 100,000 population was also high (329.17%). The analysis of the variable values based on positional statistics reveals a slightly lower differentiation in their values.

## 4. Discussion

## 5. Conclusions

## 6. Recommendations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Stages of the clustering process. Source: Own elaboration based on Wysocki [51].

**Figure 2.**Epidemic states in selected European countries from 4 March to 24 June 2020. Note: The ordinate axis shows the membership degrees of a country for states of the epidemic. Source: own elaboration based on statistical data from [44].

**Figure 3.**COVID-19 cases per 100,000 population in selected European countries from 4 March to 24 June 2020. Source: own elaboration based on statistical data from [44].

**Figure 4.**COVID-19 deaths per 100,000 population in selected European countries from 4 March to 24 June 2020. Source: own elaboration based on statistical data from [44].

**Figure 5.**Values of normalised entropy index in selected European countries. Source: own elaboration based on statistical data from [44].

**Figure 6.**Changes in daily entropy index in selected European countries from 4 March to 24 June 2020. Source: own elaboration based on statistical data from [44].

**Table 1.**Values of the selected descriptive statistics of variables characterising the epidemiological situation in the countries examined from 4 March to 24 June 2020.

Variables | Classical Measures | Positional Measures | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

min | mean | max | SD | CV | Q_{1} | Q_{2} | Q_{3} | IQR | QCOD | |

x_{1} | 0.00 | 3.04 | 490.80 | 10.00 | 329.17 | 0.16 | 0.82 | 2.65 | 2.48 | 88.41 |

x_{2} | 0.00 | 0.16 | 17.42 | 0.53 | 339.94 | 0.00 | 0.01 | 0.09 | 0.09 | 100.00 |

x_{3} | 0.00 | 6.07 | 400.00 | 16.27 | 268.05 | 0.00 | 0.72 | 6.39 | 6.39 | 100.00 |

x_{4} | 0.00 | 39.80 | 858.90 | 74.90 | 188.20 | 3.77 | 12.74 | 40.78 | 37.02 | 83.09 |

_{1}—1st quartile, Q

_{2}—median, Q

_{3}—3rd quartile, IQR—interquartile range, QCOD—quartile coefficient of dispersion (%). Source: own calculation based on statistical data from [44].

Date | States | Types of State ^{(1)} | Countries ^{(2)} |
---|---|---|---|

4 March 2020 | 1 | destabilisation | not identified |

2 | expansion | not identified | |

3 | stabilisation | France (0.98) ^{(3)}, Austria (0.97), Belarus (0.97), Belgium (0.97), Croatia (0.97), Czechia (0.97), Denmark (0.97), Estonia (0.97), Finland (0.97), Germany (0.97), Iceland (0.97), Ireland (0.97), Italy (0.97), Netherlands (0.97), Norway (0.97), Poland (0.97), Portugal (0.97), Romania (0.97), Russia (0.97), Spain (0.97), Sweden (0.97), Switzerland (0.97), Ukraine (0.97), United Kingdom (0.97), San Marino (0.84) | |

15 April 2020 | 1 | destabilisation | Germany (0.89), Netherlands (0.89), Switzerland (0.87), Portugal (0.8), Sweden (0.76), Italy (0.69), France (0.63), Denmark (0.62), Norway (0.59), Czechia (0.51) |

partial destabilisation | United Kingdom (0.48), Iceland (0.46), Luxembourg (0.43) | ||

2 | expansion | Ireland (0.70), San Marino (0.57), | |

partial expansion | Belgium (0.49), Spain (0.46) | ||

3 | stabilisation | Armenia (1.00), Kosovo (0.99), Russia (0.99), Slovakia (0.99), Ukraine (0.99), Bosnia and Herzegovina (0.99), Georgia (0.98), Lithuania (0.98), Latvia (0.98), Poland (0.96), Greece (0.94), Liechtenstein (0.94), Finland (0.92), Belarus (0.9), Malta (0.88), Bulgaria (0.87), Albania (0.82), Cyprus (0.81), Romania (0.79), Slovenia (0.79), Croatia (0.77), Moldova (0.77), Montenegro (0.72), Monaco (0.63), Serbia (0.63), Austria (0.62), Hungary (0.61), Estonia (0.54), North Macedonia (0.53), | |

24 June 2020 | 1 | destabilisation | Moldova (0.65), North Macedonia (0.65), Sweden (0.51), Belarus (0.51) |

partial destabilisation | Ireland (0.48), Russia (0.48), Lithuania (0.47) | ||

2 | expansion | Armenia (0.85) | |

3 | stabilisation | Belgium (1.00), Czechia (1.00), Denmark (1.00), Germany (1.00), Bulgaria (0.99), Serbia (0.99), Spain (0.99), Albania (0.98), Bosnia and Herzegovina (0.98), Croatia (0.98), Cyprus (0.98), Estonia (0.98), Finland (0.98), Georgia (0.98), Greece (0.98), Iceland (0.98), Luxembourg (0.98), Malta (0.98), Monaco (0.98), Montenegro (0.98), Norway (0.98), Poland (0.98), Switzerland (0.98), Ukraine (0.98), Hungary (0.97), Latvia (0.97), Liechtenstein (0.97), Slovakia (0.97), San Marino (0.96), Netherlands (0.94), Romania (0.93), Austria (0.90), Portugal (0.85), France (0.84), United Kingdom (0.80), Kosovo (0.76), Italy (0.72), Slovenia (0.72) |

^{(1)}A type of state was defined as partial, provided that the highest membership degree of the country to a specific state amounted to less than 0.5. The research also included: Armenia, Kosovo, Georgia and Cyprus.

^{(2)}Countries reporting COVID-19 in a particular period.

^{(3)}The highest membership degree of a country to the specific state. The calculations were performed with the fclust package [68] in R. Source: own elaboration based on statistical data from [44].

**Table 3.**The average values of variables for epidemic states identified in European countries (average values for fuzzy classes).

Specification | Variables | |||
---|---|---|---|---|

x_{1} | x_{2} | x_{3} | x_{4} | |

State 1 | 5.66 | 0.39 | 13.55 | 76.73 |

State 2 | 13.70 | 0.67 | 14.23 | 183.62 |

State 3 | 1.57 | 0.06 | 3.65 | 19.64 |

Mean | 3.04 | 0.16 | 6.07 | 39.80 |

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**MDPI and ACS Style**

Łuczak, A.; Kalinowski, S.
Fuzzy Clustering Methods to Identify the Epidemiological Situation and Its Changes in European Countries during COVID-19. *Entropy* **2022**, *24*, 14.
https://doi.org/10.3390/e24010014

**AMA Style**

Łuczak A, Kalinowski S.
Fuzzy Clustering Methods to Identify the Epidemiological Situation and Its Changes in European Countries during COVID-19. *Entropy*. 2022; 24(1):14.
https://doi.org/10.3390/e24010014

**Chicago/Turabian Style**

Łuczak, Aleksandra, and Sławomir Kalinowski.
2022. "Fuzzy Clustering Methods to Identify the Epidemiological Situation and Its Changes in European Countries during COVID-19" *Entropy* 24, no. 1: 14.
https://doi.org/10.3390/e24010014