Modelling the SARS-CoV-2 vaccination campaign in Italy: the fundamental role of unreported cases

Abstract

In Italy and around the world, the year 2021 was dedicated to vaccination campaigns against the COVID-19 epidemic arising after the outbreak of SARS-CoV-2 in China in 2019. In December 2020, we proposed a model prediction for the effects of vaccination, and now, after more than 9 months of the vaccination campaign, a comparison of those predictions with the actual data is mandatory. Surprising evidences emerge suggesting new strategies to consider regarding the spread of the virus and to protect frail people. After several months of the immunization campaign in Italy, it is estimated that approximately 20 000 deaths were avoided during the year 2021.

Figure 1

The fractions of reported cases in Italy, and their statistical uncertainties, as a function of the day of the year in 2021. On January 1 they were 574 767, equivalent to 100%. The magenta lines show the model scenario assuming no vaccination; this scenario was compared with the model scenario that includes the actual fit of immunizations realized to date in Italy (blue lines), as detailed in the inset image. The official data collected during the year by the Italian Ministry of Health (Ministero della Salute, 2021) and updated on October 13 are indicated by the green diamonds. Inset: bar plot of immunizations realized in Italy day by day during the year 2021 (Ministero della Salute, 2021), schematically simplified using a numerical (Gaussian) fit and introduced into the model to produce the results shown by the blue curves in the main panel.

Figure 2

The averaged values of the reported and total (reported + unreported) cases for different vaccination scenarios as a function of the day of the year in 2021. In particular the black curves represent the values of the reported + unreported cases within the no-vaccination scenario (solid black line) and the scenario that includes the actual fit of immunizations realized until now in Italy (dotted black line). The solid magenta line and blue dotted line show the averaged model results for the reported cases within the two scenarios, respectively, following the notations in Figure 1. The green diamonds show the official data (Ministero della Salute, 2021) also shown in Figure 1. Clear evidence of the role of the unreported cases for the whole year 2021 emerges.

Figure 3

The rate of the daily (asterisks) and weekly (green diamonds) averaged deaths due to COVID-19 in Italy as a function of time in the year 2021, with respect to the (reported) infected population on the same day. At a fixed average probability of death, the rate would show a constant behaviour; the evident decrease in the rate (on average) is an unambiguous indication of the effects due to vaccination.