# A Cross-Regional Analysis of the COVID-19 Spread during the 2020 Italian Vacation Period: Results from Three Computational Models Are Compared

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection

#### 2.1.1. COVID-19 Data

#### 2.1.2. Tourist Data

#### 2.1.3. Other Relevant Data

- The population density for each region (available for the year 2019);
- The annual expenditure on healthcare for each region (available for the year 2019);
- The percentage of population with more than 65 years of age (available for the year 2019);
- A categorical variable representing the geographical position of each region in Italy. ISTAT dictates that each region can belong to one of these following areas: North-West, North-East, Center, South, Islands.

#### 2.2. Methodologies

#### 2.2.1. A Changepoint Detection Method

#### 2.2.2. A Simple Toy Model

#### 2.2.3. A Statistical Model with a Negative Binomial Regression

_{0}, β

_{1}, β

_{2}, β

_{3}, β

_{4}, and β

_{5}are the coefficients to be estimated, while:

- ${Y}_{iw}$ is the cumulative number of the new infection cases, occurring in a region, $i$ during the time comprised within the (black) window, w;
- ${T}_{iw}$ is the sum of inbound and outbound tourists for a given region, $i$, during the aforementioned window, $w$;
- ${D}_{i}$ is the population density for each region, $i$, measured as the number of inhabitants per km
^{2}; - ${H}_{i}$ is the healthcare expenditure for the region, $i$, expressed as a percentage of the region’s GDP;
- ${O}_{i}$ is the ratio between the total population and the population over the age of 65;
- ${A}_{i}$ is a variable that takes into account the area to which a given region belongs, as shown in Table 2;
- $\mathrm{l}\mathrm{n}$ stands for the natural logarithm. We used logarithms at the right-hand side of the formula above, in accordance with the model proposed in [15], where this choice is mainly motivated by an increase in the performance prediction.

#### 2.2.4. A Cognitive Model

## 3. Results

#### 3.1. Where the Infection Curve Starts to Change

#### 3.2. Predicting How Big This Change Is

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Number of new daily infection cases (in blue) and correspondent seven-day moving average (orange) for each of the 21 Italian regions, in the period between 1 July and 30 September. All data was collected from the dedicated GitHub repository created by the Italian government (https://github.com/pcm-dpc/COVID-19).

**Figure 2.**Incoming domestic tourists per each Italian region for each month of 2019. The y axis is arrivals per million. Typically, peaks of the curves are observed in August.

**Figure 3.**The tourism/COVID-19 dataset, structured based on sliding windows. White are the windows used for the tourist data, black are the windows used for the cumulative count of new infected cases. The black windows are shifted 14 days forward to account for the time required for the COVID-19 symptoms to manifest.

**Figure 4.**Change points (red lines) found by the change point detection method described in Section 2.2.1. In purple are all the change points detected with a variant of the method. The daily infections curve is depicted in blue, while the correspondent seven-day moving average is in orange. Period of observation: 1 July–30 September, for each of the 21 Italian regions.

**Figure 5.**Number of new daily infection cases in Italy (blue), their 7-day moving average (orange), and the average national change point (red), falling on 1 September.

**Figure 6.**Model predictive performance: Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE).

Classification | Regions |
---|---|

North-West | Valle d’Aosta, Piedmont, Lombardy, Liguria |

North-East | Veneto, Emilia-Romagna, Friuli-Venezia Giulia, Trentino Alto-Adige |

Center | Tuscany, Lazio, Umbria, Marche |

South | Campania, Abruzzo, Molise, Puglia, Basilicata, Calabria |

Islands | Sardinia, Sicily |

**Table 2.**Coefficient Estimates for our generalized linear model (GLM). They show how tourism (T) and density (D) are highly significant, as well as the geographical indication (A) for Island and Southern regions (albeit less). The percentage of elderly (O) is also included.

Coefficients | Estimate | Std. Error | z-Value | Pr(>|z|) |
---|---|---|---|---|

(Intercept) | −9.93064 | 2.10982 | −4.707 | 2.52 × 10^{−6} |

log(T) | 0.85395 | 0.12426 | 6.872 | 6.31 × 10^{−12} |

log(D) | 0.82921 | 0.14986 | 5.533 | 3.14 × 10^{−8} |

log(H) | −1.19588 | 0.59292 | −2.017 | 0.04370 |

O | 11.12581 | 3.68649 | 3.018 | 0.00254 |

(A) Islands | 1.33754 | 0.35277 | 3.792 | 0.00015 |

(A) North-Est | 0.06887 | 0.17690 | 0.389 | 0.69705 |

(A) North-West | −0.31216 | 0.19199 | −1.626 | 0.10397 |

(A) South | 0.65365 | 0.27646 | 2.364 | 0.01806 |

**Table 3.**Structure of the Artificial Neural Network (ANN). Total number of parameters is 377, as the result of the sum of 160 + 136 + 72 + 9.

Layer (Type) | Neurons | # of Parameters |
---|---|---|

layer_1 (ReLU) | 16 | 160 (16 × 10) |

layer_2 (ReLU) | 8 | 136 (17 × 8) |

layer_3 (ReLU) | 8 | 72 (9 × 8) |

output | 1 | 9 (9 × 1) |

**Table 4.**Cumulative number of new infection cases as predicted by different models. Period: 15 August–15 September. Values in red correspond to the model with the smallest absolute error on that prediction, with respect to the other models.

Region | Real Cases | Simple Toy Model | Negative Binomial | Cognitive |
---|---|---|---|---|

Abruzzo | 480 | 270 | 463 | 293 |

Basilicata | 135 | 101 | 91 | 117 |

Calabria | 383 | 275 | 298 | 270 |

Campania | 3959 | 391 | 1466 | 2007 |

Emilia-Romagna | 3325 | 1430 | 2133 | 2484 |

Friuli Venezia Giulia | 677 | 195 | 362 | 348 |

Lazio | 4303 | 334 | 1619 | 2168 |

Liguria | 1504 | 405 | 907 | 889 |

Lombardia | 6239 | 571 | 3349 | 4329 |

Marche | 542 | 379 | 513 | 470 |

Molise | 84 | 18 | 37 | 101 |

Piemonte | 1817 | 229 | 781 | 983 |

Puglia | 1689 | 560 | 922 | 857 |

Sardegna | 1452 | 395 | 491 | 610 |

Sicilia | 1625 | 372 | 1254 | 1034 |

Toscana | 2412 | 907 | 1314 | 1557 |

Trentino-Alto Adige | 869 | 1105 | 472 | 778 |

Umbria | 546 | 212 | 223 | 199 |

Valle d’Aosta | 46 | 138 | 40 | 67 |

Veneto | 3852 | 999 | 2252 | 2557 |

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**MDPI and ACS Style**

Casini, L.; Roccetti, M. A Cross-Regional Analysis of the COVID-19 Spread during the 2020 Italian Vacation Period: Results from Three Computational Models Are Compared. *Sensors* **2020**, *20*, 7319.
https://doi.org/10.3390/s20247319

**AMA Style**

Casini L, Roccetti M. A Cross-Regional Analysis of the COVID-19 Spread during the 2020 Italian Vacation Period: Results from Three Computational Models Are Compared. *Sensors*. 2020; 20(24):7319.
https://doi.org/10.3390/s20247319

**Chicago/Turabian Style**

Casini, Luca, and Marco Roccetti. 2020. "A Cross-Regional Analysis of the COVID-19 Spread during the 2020 Italian Vacation Period: Results from Three Computational Models Are Compared" *Sensors* 20, no. 24: 7319.
https://doi.org/10.3390/s20247319