# The COVID-19 Infection in Italy: A Statistical Study of an Abnormally Severe Disease

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. COVID-19 in Italy

## 4. The IFR for COVID-19 and the Lethality in Italy

## 5. Possible Forecast of Future Behaviour of Infection

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- WHOa (World Health Organization). Rolling Updates on Coronavirus Disease (COVID-19); WHO: Geneve, Switzerland, 2020. [Google Scholar]
- Oke, J.; Heneghan, C. Global COVID-19 Case Fatality Rates; Nuffield Department of Primary Care Health Sciences: Oxford, UK, 2020; Available online: https://www.cebm.net/global-COVID-19-case-fatality-rates/ (accessed on 4 April 2020).
- Van Rossum, G.; Drake, F.L., Jr. Python Reference Manual; Centrum voor Wiskunde en Informatica: Amsterdam, The Netherlands, 1995. [Google Scholar]
- Akaike, H. New look at Statistical-Model identification. IEE Trans. on Autom. Contr.
**1974**, 19, 716–723. [Google Scholar] [CrossRef] - Cereda, D.; Tirani, M.; Rovida, F.; Demicheli, V.; Ajelli, M.; Poletti, P.; Trentini, F.; Guzzetta, G.; Marziano, V.; Barone, A.; et al. The early phase of the COVID-19 outbreak in Lombardy, Italy. arXiv
**2020**, arXiv:2003.09320. [Google Scholar] - Martuzzi, M.; Mitis, F.; Iavarone, I.; Serinelli, M. Health impact of PM10 and Ozone in 13 Italian Cities; World Health Org. Reg. Off. Eur.: Copehhagen, Denmark, 2006; ISBN 92-890-2293-0. [Google Scholar]
- Stafoggia, M.; Faustin, A.; Rognin, M.; Tessari, R.; Cadum, E.; Pacelli, B.; Pandolfi, P.; Miglio, R.; Mallone, S.; Vigotti, M.A.; et al. Gruppo collaborativo EpiAri. Epidemiol Prev.
**2009**, 33 (Suppl. S1), 65–76. [Google Scholar] [PubMed] - Department of Italian Civil Protection Repository. Available online: http://www.protezionecivile.gov.it/attivita-rischi/rischio-sanitario/emergenze/coronavirus (accessed on 4 May 2020).
- Lavezzo, E.; Franchin, E.; Ciavarella, C.; Cuomo-Dannenburg, G.; Barzon, L.; Del Vecchio, C.; Rossi, L.; Manganelli, R.; Loregian, A.; Navarin, N.; et al. Suppression of COVID-19 outbreak in the municipality of Vo’, Italy. MedarXiv
**2020**. [Google Scholar] [CrossRef][Green Version] - Moriarty, L.F.; Plucinski, M.M.; Marston, B.J.; Kurbatova, E.V.; Knust, B.; Murray, E.L.; Pesik, N.; Rose, D.; Fitter, D.; Kobayashi, M.; et al. Public Health Responses to COVID-19 Outbreaks on Cruise Ships-Worldwide. MMWR
**2020**, 69, 12. [Google Scholar] [CrossRef] - Russell, T.W.; Hellewell, J.; Jarvis, C.I.; Van Zandvoort, K.; Abbott, S.; Ratnayake, R.; CMMID COVID-19 Working Group; Flasche, S.; Eggo, R.M.; Edmunds, W.J.; et al. Estimating the infection and case fatality ratio for coronavirus disease (COVID-19) using age-adjusted data from the outbreak on the Diamond Princess cruise ship, February 2020. Euro Surveill.
**2020**, 25. [Google Scholar] [CrossRef][Green Version] - Flaxman, S.; Mishra, S.; Gandy, A.; Unwin, H.; Coupland, H.; Mellan, T.; Zhu, H.; Berah, T.; Eaton, J.; Perez Guzman, P.; et al. Report 13: Estimating the Number of Infections and the Impact of Non-Pharmaceutical Interventions on COVID-19 in 11 European Countries; Technical Report; Imperial College COVID-19 Response Team: London, UK, 2020. [Google Scholar] [CrossRef]
- Chen, N.; Zhou, M.; Dong, X.; Qu, J.; Gong, F.; Han, Y.; Qiu, Y.; Wang, J.; Wei, Y.; Xia, J.; et al. Epidemiological and Clinical Characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: A descriptive study. Lancet
**2020**, 395, 507–513. [Google Scholar] [CrossRef][Green Version] - Chen, R.; Chu, C.; Tan, J.; CaoSong, W.; Xu, X.; Jing, C.; Ma, W.; Yang, C.; Chen, B.; Gui, Y.; et al. Ambient air pollution and hospital admission in Shangai, China. J. Hazard. Mater.
**2010**, 181, 234–240. [Google Scholar] [CrossRef] [PubMed] - Ye, X.; Peng, L.; Kan, H.; Wang, W.; Geng, F.; Mu, Z.; Zhou, J.; Yang, D. Acute Effects of Particulate Air Pollution on the Incidence of Coronary Heart Disease in Shanghai, China. PLoS ONE
**2016**, 11, e0151119. [Google Scholar] [CrossRef] [PubMed] - Dominici, F.; Peng, R.D.; Bell, M.L.; Pham, L.; McDermott, A.; Zeger, S.L.; Samet, J.M. Fine Particulate Air Pollution and Hospital Admission for Cardiovascular and Respiratory Diseases. JAMA
**2006**, 295, 1127–1134. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ciencewicki, J.; Jaspers, I. Air Pollution and Respiratory Viral Infection. Inhal. Toxicol.
**2007**, 19, 1135–1146. [Google Scholar] [CrossRef] [PubMed] - Soggiu, M.E.; Settimo, G. L’incerta Correlazione tra Inquinamento Atmosferico e l’epidemia da COVID-19. 2020. Available online: https://www.iss.it/en/primo-piano/-/asset_publisher/o4oGR9qmvUz9/content/id/5355820 (accessed on 29 April 2020). (In Italian).
- WHOb (World Health Organization). World Health Statistics Tabacco Smoking; WHO: Geneve, Switzerland, 2016. [Google Scholar]
- ISSa. (Istituto Superiore di Sanità). 2019. Antibiotico Resistenza. 2019. Available online: https://www.epicentro.iss.it/antibiotico-resistenza/epidemiologia-europa (accessed on 4 April 2020). (In Italian).
- Jin, Y.; Cai, L.; Cheng, Z.; Cheng, H.; Deng, T.; Fan, Y.P.; Fang, C.; Huang, D.; Huang, L.Q.; Huang, Q.; et al. A rapid advice guideline for the diagnosis and treatment of 2019 novel coronavirus (2019-nCoV) infected pneumonia (standard version). Mil. Med. Res.
**2020**, 7, 4. [Google Scholar] [CrossRef] [PubMed][Green Version] - ISTATa. (Istituto Nazionale di Statistica). 2020. Decessi e Cause di Morte. Available online: https://www.istat.it/it/archivio/240401 (accessed on 4 April 2020). (In Italian).
- Koch Institute. Report on the Epidemiology of Influenza in Germany 2018/2019. 2019. Available online: https://www.rki.de/EN/Content/infections/epidemiology/inf_dis_Germany/influenza/summary_2018-19.html (accessed on 4 April 2020).
- ISSb. (Istituto Superiore di Sanità). 2020. Infografica March 25th, 2020. Available online: https://www.epicentro.iss.it/coronavirus/bollettino/Infografica_25marzo%20ITA.pdf (accessed on 4 April 2020).
- Wang, D.; Hu, B.; Hu, C.; Zhu, F.; Liu, X.; Zhang, J.; Wang, B.; Xiang, H.; Cheng, Z.; Xiong, Y.; et al. Clinical characteristics of 138 hospitalized patients with 2019 novel coronavirus-infected pneumonia in Wuhan, China. JAMA
**2020**, 323, 1061–1069. [Google Scholar] [CrossRef] [PubMed] - Gatto, M.; Bertuzzo, E.; Mari, L.; Miccoli, S.; Carraro, L.; Casagrandi, R.; Rinaldo, A. Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures. Proc. Natl. Acad. Sci. USA
**2020**, 117, 10484–10491. [Google Scholar] [CrossRef] [PubMed][Green Version] - Lauer, S.A.; Grantz, K.H.; Bi, Q.; Jones, F.K.; Zheng, Q.; Meredith, H.R.; Azman, A.S.; Reich, N.G.; Lessler, J. The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application. Ann. Intern. Med.
**2020**, 172, 577–582. [Google Scholar] [CrossRef] [PubMed][Green Version] - WHOc (World Health Organization). Coronavirus Disease 2019 (COVID-19) Situation Report 1–73; WHO: Geneve, Switzerland, 2020. [Google Scholar]
- ISSc. (Istituto Superiore di Sanità). 2020. Characteristics of SARS-CoV-2 Patients Dying in Italy. Available online: https://www.epicentro.iss.it/en/coronavirus/bollettino/Report-COVID-2019_20_april_2020.pdf (accessed on 20 April 2020).
- Wang, W.; Tang, J.; Wei, F. Updated understanding of the outbreak of 2019 novel coronavirus (2019-nCoV) in Wuhan, China. J. Med. Virol.
**2020**, 92, 441–447. [Google Scholar] [CrossRef] [PubMed][Green Version] - Johns Hopkins University Coronavirus Resource Center. 2020. Available online: https://coronavirus.jhu.edu/map.html (accessed on 4 April 2020).
- Gompertz, B. On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies. Phil. Trans. Roy. Soc. London
**1832**, 123, 513–585. [Google Scholar] - Janoschek, A. Das reaktionskinetische Grundgesetz und seine Beziehungen zum Wachstums—und Ertragsgesetz. Stat. Vjschr
**1957**, 10, 25–37. (In German) [Google Scholar] - Richards, F.J. A Flexible Growth Function for Empirical Use. J. Exp. Botany
**1959**, 10, 290–301. [Google Scholar] [CrossRef] - ISTATb. (Istituto Nazionale di Statistica). Spostamenti Quotidiani e Nuove Forme di Mobilita. 2018, p. 20. Available online: https://www.istat.it/it/files//2018/11/Report-mobilit%C3%A0-sostenibile.pdf (accessed on 4 April 2020). (In Italian).
- ISSd. (Istituto Superiore di Sanità). 2020. Survey Nazionale sul Contagio COVID-19 Nelle Strutture Residenziali e Sociosanitarie, Third Report. Available online: https://www.epicentro.iss.it/coronavirus/pdf/sars-cov-2-survey-rsa-rapporto-3.pdf (accessed on 20 April 2020). (In Italian).
- Adda, J. Economic Activity and the Spread of Viral Diseases: Evidence from High Frequency Data. Quart. J. Econ.
**2016**, 131, 891–941. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Total COVID-19 cases reported in Italy from 24 February to 30 March 2020 according to Protezione Civile (black dots) with logistic (blue solid line), exponential (red solid line), and cubic (green solid line) infection rates. Dotted black vertical lines mark the dates of Italian school lockdown and the nationwide total lockdown; the asterisk indicates that the exponential and the cubic fits are based on data until 12 March: score from Akaike Information Criterion (AIC) test (not reported) on logistic, cubic, and exponential fits shows higher reliability of the first two after this date and for the logistic against the cubic after 25 March 2020. (

**a**) Fits obtained from the data in semi-logarithmic scale; (

**b**) same data and fits shown in linear scale. Fit parameters: Logistic $(y=K\frac{1+m{e}^{xr}}{1+n{e}^{xr}};K=\left(135\pm 2\right)\xb7{10}^{3},\text{}m=-1.4\pm 0.2,\text{}n=170\pm 9,\text{}r=0.174\pm 0.003);$ Exponential $\left(y=A{e}^{Bx};A=410\pm 30,\text{}B=0.2\pm 0.01;Cubic=a+bx+c{x}^{2}+d{x}^{3};a=-40\pm 20,\text{}b=36\pm 8,\text{}c=-6.7\pm 0.9,\text{}d=0.44\pm 0.03\right).$

**Figure 2.**Total COVID-19 cases reported in China from 22 January to 31 March 2020 according to the Johns Hopkins University data repository. Circles, squares, and triangles represent total COVID-19 cases registered in China, the region of Hubei, and China without Hubei; red, black, and blue dashed lines are the associated logistic fits. Shaded areas represent the family of curves obtainable by making the fit parameters vary within their confidence intervals. Fit parameters: Logistic $(y=K\frac{1+m{e}^{-xr}}{1+n{e}^{-xr}};China:K\text{}=\left(811\pm 3\right)\xb7{10}^{2},\text{}m=-0.9\pm 0.6,\text{}n=53\pm 9,\text{}r=0.214\pm 0.008);$ $Hubei:\text{}K=\left(678\pm 3\right)\xb7{10}^{2},\text{}m=-0.4\pm 1.2,\text{}n=100\pm 20,\text{}r=0.232\pm 0.01;$ $China\text{}wihtout\text{}Hubei:\text{}K=\left(131.6\pm 0.3\right)\xb7{10}^{3},\text{}m=-1.4\pm 0.11,\text{}n=14\pm 1.4,r=0.208\pm 0.006).$

**Figure 3.**Deaths reported by Italian Civil Protection. (

**a**) Total deaths reported in Italy (green dots), Lombardia (blue dots), and Italy without Lombardia (red dots) from 24 February to 30 March 2020 and the corresponding logistic fit in solid lines. Dotted vertical lines mark the dates of Italian school lockdown and Italy total lockdown. A sample best fitting Richards’ curve for the whole Italy is also shown (green dotted line). (

**b**) Same as in (

**a**) using the new daily reported deaths and fitting the derivate of the logistic and Richards’ curve. Shaded areas represent the family of curves obtainable by making the fit parameters vary within their confidence intervals. Fit parameters: Logistic $(y=K\frac{1+m{e}^{-xr}}{1+n{e}^{-xr}};Logisti{c}^{\prime}:\text{}\frac{Kr\left(m-n\right){e}^{-xr}}{{\left({e}^{rx}+n\right)}^{2}};Italy:\text{}K=\left(178\pm 4\right)\xb7{10}^{2},\text{}m=-3.1\pm 0.5,n=380\pm 30,\text{}r=0.183\pm 0.004);$ Lombardia: $K=\left(100\pm 4\right)\xb7{10}^{2},\text{}m=-2.8\pm 0.5,\text{}n=270\pm 30,r=0.176\pm 0.006);$ Italy without Lombardia: $K=\left(74\pm 2\right)\xb7{10}^{2},\text{}m=-4.0\pm 0.8,\text{}n=740\pm 60,r=0.201\pm 0.004;$ $\mathrm{Richards}(y=\frac{K}{{\left(1+{e}^{-B\left(x-t\right)}\right)}^{\frac{1}{\nu}}};{y}^{\prime}:\frac{BK{e}^{\left(t-x\right)}{({e}^{\left(t-x\right)}+1)}^{\frac{-\left(\nu +1\right)}{\nu}}}{\nu};Italy:\text{}K=\left(276\pm 5\right)\xb7{10}^{2},$ $\text{}B=0.1\pm 0.5,t=20\pm 30,\text{}\nu =0.196\pm 0.004).$

**Figure 4.**Deaths reported by Italian Civil Protection for Emilia-Romagna and Calabria regions. (

**a**) Total, cumulative deaths reported in Emilia-Romagna (red dots) and in Calabria (blue dots) from 24 February to 30 March 2020 according to Italian Civil Protection and the corresponding logistic fit obtained from the data. Dotted vertical lines mark the dates of Italian school lockdown and Italy total lockdown. (

**b**) Same as in (

**a**) using the new daily reported deaths and fitting the derivate of the logistic curve. Shaded areas represent the family of curves obtainable by making the fit parameters vary within their confidence intervals. Note: the left and the right y-axes scales refer to the Emilia-Romagna and the Calabria curves, respectively. Fit parameters: Logistic $(y=K\frac{1+m{e}^{-xr}}{1+n{e}^{-xr}};Logisti{c}^{\prime}:\text{}\frac{Kr\left(m-n\right){e}^{-xr}}{{\left({e}^{rx}+n\right)}^{2}};;Emilia-Romagna:\text{}K=1970\pm 40,\text{}m=-3.0\pm 0.6,n=360\pm 30,\text{}r=0.197\pm 0.004);$ $\text{}Calabria:\text{}K=100\pm 20,\text{}m=-30\pm 13,\text{}n=\left(12\pm 3\right)\xb7{10}^{3},r=0.208\pm 0.006).$

**Figure 5.**Estimated (total and undetected) COVID-19 cases in Italy based on three different infection fatality ratio (IFR) hypotheses: 0.2% (blue and light blue lines), 1.3% (red and pink lines), and 5.7% (green and light green lines). Blue and sky-blue solid lines represent logistic fits of total and undetected estimated cases with IFR = 0.2%, respectively. Red and pink solid lines represent logistic fits of total and undetected estimated cases with IFR = 1.3%, respectively. Green and light green solid lines represent logistic fits of total and undetected estimated cases with IFR = 5.7%, respectively. Black dotted vertical lines mark the dates of Codogno area lockdown, Italian schools’ lockdown, Lombardia lockdown, and Italy lockdown. Dark orange dashed vertical line marks the inflection points of the three curves representing the total infected estimates; magenta dotted vertical line marks the 95% of the plateau of the three curves. Shaded areas represent the family of curves obtainable by making the fit parameters vary within their confidence intervals. Best fit parameters are listed in Table 2.

**Table 1.**Numbers of recorded infections and deaths in several countries as of 30 March 2020. Also indicated is the CFR (case fatality ratio) defined as the ratio between the number of deaths and the number of recorded cases.

Country | Cases | Deaths | CFR (%) |
---|---|---|---|

Lombardia (Italy) | 42,161 | 6818 | 16.1 |

Italy | 101,739 | 11,591 | 11.3 |

Spain | 87,956 | 7716 | 8.77 |

Netherlands | 11,750 | 864 | 7.35 |

France | 44,550 | 3024 | 6.78 |

Iran | 41,495 | 2757 | 6.64 |

UK | 22,141 | 1408 | 6.35 |

Belgium | 11,899 | 513 | 4.31 |

China | 81,518 | 3305 | 4.05 |

Sweden | 4028 | 146 | 3.62 |

Denmark | 2577 | 77 | 3.53 |

Japan | 2178 | 57 | 2.61 |

Switzerland | 15,922 | 359 | 2.25 |

USA | 163,788 | 3141 | 1.91 |

Ireland | 2910 | 54 | 1.80 |

South Korea | 9661 | 158 | 1.63 |

Turkey | 10,827 | 168 | 1.55 |

Canada | 7448 | 89 | 1.19 |

Austria | 9618 | 108 | 1.12 |

Portugal | 6408 | 140 | 1.11 |

Germany | 66,885 | 645 | 0.96 |

Norway | 4445 | 32 | 0.71 |

Australia | 4460 | 19 | 0.42 |

Israel | 4695 | 16 | 0.34 |

**Table 2.**Logistic fit $(y=K\frac{1+m{e}^{-xr}}{1+n{e}^{-xr}})$ parameters for the estimated (total and undetected) COVID-19 cases in Italy based on three different IFR hypotheses: 0.2% (blue and light blue dots), 1.3% (red and pink dots), and 5.7% (green and light green dots) (see Figure 5).

Total Estimated Cases (IFR 0.2 %) | |||

K: (81 ± 1.6)∙10^{5} | m: −3.7 ± 0.7 | q : 860 ± 60 | r : 0.211 ± 0.003 |

Total Undetected Cases (IFR 0.2 %) | |||

K: (80 ± 1.6)∙10^{5} | m: −3.7 ± 0.7 | q : 860 ± 60 | r : 0.211 ± 0.003 |

Total Estimated Cases (IFR 1.3 %) | |||

K: (137 ± 3)∙10^{4} | m: −3.1 ± 0.5 | n : 380 ± 30 | r: 0.184 ± 0.004 |

Total Undetected Cases (IFR 1.3 %) | |||

K: (132 ± 3)∙10^{4} | m: −3.1 ± 0.5 | n: 380 ± 30 | r: 0.183 ± 0.004 |

Total Estimated Cases (IFR 5.7 %) | |||

K: (290 ± 9) ∙10^{3} | m: −3.6 ± 0.6 | n: 890 ± 50 | r: 0.213 ± 0.003 |

Total Undetected Cases (IFR 5.7 %) | |||

K: (260 ± 6) ∙10^{3} | m: −3.4 ± 0.6 | n: 860 ± 50 | r: 0.215 ± 0.003 |

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## Share and Cite

**MDPI and ACS Style**

De Natale, G.; Ricciardi, V.; De Luca, G.; De Natale, D.; Di Meglio, G.; Ferragamo, A.; Marchitelli, V.; Piccolo, A.; Scala, A.; Somma, R.; Spina, E.; Troise, C. The COVID-19 Infection in Italy: A Statistical Study of an Abnormally Severe Disease. *J. Clin. Med.* **2020**, *9*, 1564.
https://doi.org/10.3390/jcm9051564

**AMA Style**

De Natale G, Ricciardi V, De Luca G, De Natale D, Di Meglio G, Ferragamo A, Marchitelli V, Piccolo A, Scala A, Somma R, Spina E, Troise C. The COVID-19 Infection in Italy: A Statistical Study of an Abnormally Severe Disease. *Journal of Clinical Medicine*. 2020; 9(5):1564.
https://doi.org/10.3390/jcm9051564

**Chicago/Turabian Style**

De Natale, Giuseppe, Valerio Ricciardi, Gabriele De Luca, Dario De Natale, Giovanni Di Meglio, Antonio Ferragamo, Vito Marchitelli, Andrea Piccolo, Antonio Scala, Renato Somma, Emanuele Spina, and Claudia Troise. 2020. "The COVID-19 Infection in Italy: A Statistical Study of an Abnormally Severe Disease" *Journal of Clinical Medicine* 9, no. 5: 1564.
https://doi.org/10.3390/jcm9051564