The COVID-19 outbreak has stimulated the interest in the proposal of novel epidemiological models to predict the course of the epidemic so as to help planning effective control strategies. In particular, in order to properly interpret the available data, it has become clear that one must go beyond most classic epidemiological models and consider models that, like the recently proposed SIDARTHE, offer a richer description of the stages of infection. The problem of learning the parameters of these models is of crucial importance especially when assuming that they are time-variant, which further enriches their effectiveness. In this paper we propose a general approach for learning time-variant parameters of dynamic compartmental models from epidemic data. We formulate the problem in terms of a functional risk that depends on the learning variables through the solutions of a dynamic system. The resulting variational problem is then solved by using a gradient flow on a suitable, regularized functional. We forecast the epidemic evolution in Italy and France. Results indicate that the model provides reliable and challenging predictions over all available data as well as the fundamental role of the chosen strategy on the time-variant parameters.
翻译:COVID-19疫情的爆发激发了人们对新的流行病学模型提案的兴趣,这些模型旨在预测流行病的走向,从而帮助规划有效的控制战略,特别是,为了正确解释现有数据,人们显然必须超越最典型的流行病学模型,考虑像最近提议的SIDARMETH这样的模型,对感染阶段的描述更为丰富。了解这些模型参数的问题至关重要,特别是在假设这些模型具有时间差异,从而进一步丰富了其有效性的情况下。在本文件中,我们提出了一个从流行病数据中学习动态区际模型的时间差异参数的一般方法。我们从功能风险的角度来提出问题,这种风险取决于通过动态系统的解决办法学习变量。由此产生的变化问题随后通过在适当的、正规功能上使用梯度流来解决。我们预报意大利和法国的流行病演变情况。结果显示,该模型对所有可获得的数据以及所选择的战略在时间差异参数上的基本作用提供了可靠和具有挑战性的预测。