The purpose of this work is to give a contribution to the understanding of the COVID-19 contagion in Italy. To this end, we developed a modified Susceptible-Infected-Recovered-Deceased (SIRD) model for the contagion, and we used official data of the pandemic for identifying the parameters of this model. Our approach features two main non-standard aspects. The first one is that model parameters can be time-varying, allowing us to capture possible changes of the epidemic behavior, due for example to containment measures enforced by authorities or modifications of the epidemic characteristics and to the effect of advanced antiviral treatments. The time-varying parameters are written as linear combinations of basis functions and are then inferred from data using sparse identification techniques. The second non-standard aspect resides in the fact that we consider as model parameters also the initial number of susceptible individuals, as well as the proportionality factor relating the detected number of positives with the actual (and unknown) number of infected individuals. Identifying the model parameters amounts to a non-convex identification problem that we solve by means of a nested approach, consisting in a one-dimensional grid search in the outer loop, with a Lasso optimization problem in the inner step.

这项工作的目的是为理解意大利的COVID-19传染病做出贡献。为此，我们开发了一种针对传染病的改良的易感感染-恢复-死亡（SIRD）模型，并使用大流行病的官方数据来确定该模型的参数。我们的方法具有两个主要的非标准方面。第一个是模型参数可以随时间变化，从而使我们能够捕获流行病行为的可能变化，例如由于当局实施的围堵措施或流行病特征的修改以及先进的抗病毒治疗的效果。时变参数被写为基函数的线性组合，然后使用稀疏识别技术从数据中推断出来。第二个非标准方面在于，我们还将易感个体的初始数量以及与检测到的阳性数量与实际（和未知）感染个体数量相关的比例因子视为模型参数。识别模型参数相当于一个非凸识别问题，我们通过嵌套方法解决了这个问题，该方法包括在外循环中进行一维网格搜索，并在内部步骤中进行套索优化。