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 (SIR) model for the contagion, and we used official data of the pandemic up to March 30th, 2020 for identifying the parameters of this model. The non standard part of our approach resides in the fact that we considered 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 contagion, recovery and death rates as well as the mentioned parameters amounts to a non-convex identification problem that we solved by means of a two-dimensional grid search in the outer loop, with a standard weighted least-squares optimization problem as the inner step.

中文翻译：

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意大利 COVID-19 传染病的改进 SIR 模型

这项工作的目的是为了解意大利的 COVID-19 传染病做出贡献。为此，我们为传染病开发了一个经过修改的易感感染恢复 (SIR) 模型，我们使用截至 2020 年 3 月 30 日的大流行官方数据来确定该模型的参数。我们方法的非标准部分在于，我们还将易感个体的初始数量以及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。识别传染率、恢复率和死亡率以及上述参数相当于一个非凸识别问题，我们通过外循环中的二维网格搜索解决了这个问题，