Department of Information Engineering, University of Padova, Padova, Italy.
Department of Molecular Medicine, Professor Emeritus, University of Padova, Padova, Italy.
Sci Rep. 2021 May 7;11(1):9772. doi: 10.1038/s41598-021-89014-9.
Understanding the SARS-CoV-2 dynamics has been subject of intense research in the last months. In particular, accurate modeling of lockdown effects on human behaviour and epidemic evolution is a key issue in order e.g. to inform health-care decisions on emergency management. In this regard, the compartmental and spatial models so far proposed use parametric descriptions of the contact rate, often assuming a time-invariant effect of the lockdown. In this paper we show that these assumptions may lead to erroneous evaluations on the ongoing pandemic. Thus, we develop a new class of nonparametric compartmental models able to describe how the impact of the lockdown varies in time. Our estimation strategy does not require significant Bayes prior information and exploits regularization theory. Hospitalized data are mapped into an infinite-dimensional space, hence obtaining a function which takes into account also how social distancing measures and people's growing awareness of infection's risk evolves as time progresses. This also permits to reconstruct a continuous-time profile of SARS-CoV-2 reproduction number with a resolution never reached before in the literature. When applied to data collected in Lombardy, the most affected Italian region, our model illustrates how people behaviour changed during the restrictions and its importance to contain the epidemic. Results also indicate that, at the end of the lockdown, around [Formula: see text] of people in Lombardy and [Formula: see text] in Italy was affected by SARS-CoV-2, with the fatality rate being 1.14%. Then, we discuss how the situation evolved after the end of the lockdown showing that the reproduction number dangerously increased in the summer, due to holiday relax, reaching values larger than one on August 1, 2020. Finally, we also document how Italy faced the second wave of infection in the last part of 2020. Since several countries still observe a growing epidemic and others could be subject to other waves, the proposed reproduction number tracking methodology can be of great help to health care authorities to prevent SARS-CoV-2 diffusion or to assess the impact of lockdown restrictions on human behaviour to contain the spread.
了解 SARS-CoV-2 的动力学一直是过去几个月研究的热点。特别是，准确建模封锁对人类行为和疫情演变的影响是一个关键问题，例如为紧急管理中的医疗保健决策提供信息。在这方面，迄今为止提出的房室和空间模型使用接触率的参数描述，通常假设封锁的时间不变效应。在本文中，我们表明这些假设可能导致对正在进行的大流行的错误评估。因此，我们开发了一类新的非参数房室模型，能够描述封锁的影响随时间如何变化。我们的估计策略不需要大量贝叶斯先验信息，并利用正则化理论。住院数据映射到无限维空间，从而获得一个函数，该函数还考虑了随着时间的推移社交距离措施和人们对感染风险的认识的变化。这还允许以前在文献中从未达到过的分辨率重建 SARS-CoV-2 繁殖数的连续时间分布。当应用于在意大利受影响最严重的伦巴第大区收集的数据时，我们的模型说明了在限制期间人们的行为如何变化及其对遏制疫情的重要性。结果还表明，在封锁结束时，伦巴第大区约有 [Formula: see text] 的人受到 SARS-CoV-2 的影响，意大利约有 [Formula: see text] 的人受到影响，死亡率为 1.14%。然后，我们讨论了封锁结束后情况的演变，表明由于假期放松，繁殖数在夏季危险地增加，2020 年 8 月 1 日达到 1 以上。最后，我们还记录了意大利如何在 2020 年底应对第二波感染。由于几个国家的疫情仍在增长，其他国家可能会受到其他波的影响，因此提出的繁殖数跟踪方法可以为卫生保健当局提供很大帮助，以防止 SARS-CoV-2 的传播，或评估封锁限制对人类行为的影响以遏制传播。
