When the COVID-19 pandemic first emerged in early 2020, healthcare and bureaucratic systems worldwide were caught off guard and largely unprepared to deal with the scale and severity of the outbreak. In Italy, this led to a severe underreporting of infections during the first wave of the spread. The lack of accurate data is critical as it hampers the retrospective assessment of nonpharmacological interventions, the comparison with the following waves, and the estimation and validation of epidemiological models. In particular, during the first wave, reported cases of new infections were strikingly low if compared with their effects in terms of deaths, hospitalizations and intensive care admissions. In this paper, we observe that the hospital admissions during the second wave were very well explained by the convolution of the reported daily infections with an exponential kernel. By formulating the estimation of the actual infections during the first wave as an inverse problem, its solution by a regularization approach is proposed and validated. In this way, it was possible to computed corrected time series of daily infections for each age class. The new estimates are consistent with the serological survey published in June 2020 by the National Institute of Statistics (ISTAT) and can be used to speculate on the total number of infections occurring in Italy during 2020, which appears to be about double the number officially recorded.

翻译：2020年初COVID-19大流行首次出现时，全球医疗和行政系统措手不及，且普遍未能充分应对疫情的规模与严重性。在意大利，这导致第一波传播期间感染病例被严重漏报。缺乏准确数据的问题十分严峻，因为它阻碍了对非药物干预措施的回顾性评估、与后续疫情波的比较，以及流行病学模型的估算与验证。特别是，在第一波疫情期间，报告的新感染病例数量与其导致的死亡、住院及重症监护入院等后果相比，明显偏低。本文观察到，第二波疫情中的医院入院数据可通过报告日感染量与指数核的卷积得到良好解释。通过将第一波疫情期间实际感染量的估算构建为逆问题，提出并验证了基于正则化方法的求解方案。由此，能够为各年龄类别计算修正后的日感染量时间序列。新的估算结果与意大利国家统计局（ISTAT）于2020年6月发布的血清学调查一致，并可据此推测2020年意大利实际发生的总感染人数——该数字约为官方记录的两倍。