Tracking the time course of reproduction number and lockdown's effect on human behaviour during SARS-CoV-2 epidemic: nonparametric estimation.

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.