Advanced forecasting of SARS-CoV-2-related deaths in Italy, Germany, Spain, and New York State.

To the Editor,

An appropriate forecasting model can contribute to define strategic choices both in limiting the spread of SARS‐Cov‐2 virus and in reducing the related mortality rate. Temporal trends of SARS‐CoV‐2 key epidemiological indicators (eg, mortality, incidence of infected cases) to describe the ongoing pandemic caused by SARS‐CoV‐2 have been estimated , , ; their accuracy is key to plan and implement adequate health interventions (eg, increasing ICU availability, distribute personal protection gear, an eventual vaccine). A number of studies tried to identify the best model to forecast SARS‐Cov‐2‐related deaths, interpolating daily cases according to a Gaussian curve. Recently, we suggested an innovative and robust data mining approach based on Chinese and Italian data to forecast SARS‐Cov‐2‐related mortality using a 3rd‐degree polynomial curve, which describes a growth up to the daily peak, and, then, a five parameter logistic (5PL) asymmetrical sigmoidal curve following a parametric growth (45% of aggregated cases at the peak day, which is at 20% of the estimated aggregated outbreak duration; 50% of total cases at 20.8% of the expected duration; 63.3% of total cases at 24% of the expected duration; 81.4% at 30% of the expected duration; 92.8% at 40% of the expected duration; 99.5% at 80% of the expected duration). Based on this, we derived a reliable model which was obtained by the analysis and interpolation of the aggregated cases since we do not expect a symmetric behavior of the curve after the daily peaks due to effect of different factors (eg, the social intervention, political measures, increase in ICU beds).

Based on this model, we aimed at predicting SARS‐Cov‐2‐related mortality in Italy, Germany, Spain, and New York State. To validate the model, we calculated R2 correlations for Italy (0.995), Germany (0.996), Spain (0.988), and New York State (0.998) after 30, 18, 11, and 10 days of prediction, respectively, thus confirming the reliability of our modeling approach during the first month of this outbreak in each of these countries (Figure 1A).

Figure 1

A, The model accuracy curve is achieved using a 3rd‐grade polynomial curve in Italy, Germany, Spain, and New York State. It highlights the differences between real and simulated data after inputting the first 17 d. B, The curves depicting the predictions of the expected deaths are obtained by a 3rd‐grade polynomial curve up to daily peak and later by a parametric 5PL asymmetrical sigmoidal. The predictions are calculated starting from the first 17 d. The curve of expected deaths per country splits considering the number of days supposed to reach daily peak after the lockdown (28 d: upper curve; 21 d: lower curve)

Accordingly, the expected number of SARS‐Cov‐2‐related deaths up to May 31, 2020, was associated with a curve suggesting no consistent correlation between the number of deaths and the size of the national population (Figure 1B). Instead, the expected SARS‐Cov‐2‐related mortality is more closely related to early events within the first days of the outbreak and to timing to regional/national interventions (eg, social distancing, confinement), which suggests that superspreading events (eg Lombardia region, Italy) deeply impact on the magnitude of the curve and, in turn, on the number of deaths.

Importantly, the forecast is in keep with the number of days supposed to reach daily peak after the lockdown measures. Figure 1B illustrates the curves of the expected deaths based on daily peak after 28 and 21 days in Italy, Germany, Spain, and New York State. Based on this and provided current public health intervention remain unchanged, our model would predict by May 31st two different scenarios, high and low, for each country, specifically: Italy: a high of 50 562 ± 1264, and a low of 29 525 ± 738; Germany: a high of 11 400 ± 285, and a low of 5776 ± 144; Spain: a high of 54 867 ± 1372, and a low of 27 730 ± 693; and New York State: a high of 36 475 ± 912, and a low of 17 146 ± 429 of deaths.

Taken together, these findings suggest that for both Italy and Spain, early superspreading events (eg, Codogno, a town located in Lombardia, and the Atalanta Bergamo vs FC Valencia football match in Milan on February 19th, Women's Day marches, Madrid, March 4th) have favored the increased number of deaths compared to Germany where such events occurred on a smaller scale (eg carnival, Heinsberg, Germany, February 15th, and the so‐called Westport soirée—Party Zero on March 5th, Westport, CT, USA).

Despite being an advanced prediction, some limitations should be underscored, from an intrinsic wider uncertainty due to the fact that the underlying conditions can change to the possibility that interventions might be implemented based on such predictions, then changing the predicted outcome. We, therefore, recommend to carefully consider those estimates but with caution based on the above‐mentioned uncertainties.

Our predictions were estimated for Italy, Germany, Spain, and New York State but can be translated to other settings. Based on this, it might also be possible to predict the number of respirators, health personnel needed and further spreading, downscaling, or healing curves but that would require additional data. For this purpose, positive cases would have to be monitored, for, for example, a 2‐week period and % of hospitalized and % of ICU patients assessed. These results, however, are heavily influenced by local factors such as the number of nondetected but infected patients, availability of hospital and ICU beds, local treatment protocols, and lack of prompt reporting of those recovered. The implications of our results highlight the key role of early spreading events during this SARS‐CoV‐2 pandemic and would call for rapid public health actions in future outbreaks.

CONFLICT OF INTEREST

Dr Virchow, Dr Soriano, Dr Canonica, Dr Miozzo, Dr Centanni, Dr Gerli, and Dr Sotgui have nothing to disclose.