In this paper, we propose a parameter identification methodology of the SIRD model, an extension of the classical SIR model, that considers the deceased as a separate category. In addition, our model includes one parameter which is the ratio between the real total number of infected and the number of infected that were documented in the official statistics. Due to many factors, like governmental decisions, several variants circulating, opening and closing of schools, the typical assumption that the parameters of the model stay constant for long periods of time is not realistic. Thus our objective is to create a method which works for short periods of time. In this scope, we approach the estimation relying on the previous 7 days of data and then use the identified parameters to make predictions. To perform the estimation of the parameters we propose the average of an ensemble of neural networks. Each neural network is constructed based on a database built by solving the SIRD for 7 days, with random parameters. In this way, the networks learn the parameters from the solution of the SIRD model. Lastly we use the ensemble to get estimates of the parameters from the real data of Covid19 in Romania and then we illustrate the predictions for different periods of time, from 10 up to 45 days, for the number of deaths. The main goal was to apply this approach on the analysis of COVID-19 evolution in Romania, but this was also exemplified on other countries like Hungary, Czech Republic and Poland with similar results. The results are backed by a theorem which guarantees that we can recover the parameters of the model from the reported data. We believe this methodology can be used as a general tool for dealing with short term predictions of infectious diseases or in other compartmental models.
翻译:本文提出了一种SIRD模型的参数辨识方法,该模型是经典SIR模型的扩展,将死亡病例单独作为一个类别。此外,我们的模型引入了一个参数,即实际感染者总数与官方统计中记录感染者数量之比。由于政府决策、多种变异毒株流行、学校开放与关闭等诸多因素,认为模型参数长期保持不变的典型假设并不现实。因此,我们的目标是建立一种适用于短时间尺度的方法。在此框架下,我们基于前7天的数据进行参数估计,并利用辨识出的参数进行预测。为执行参数估计,我们采用多个神经网络集成的平均值方法。每个神经网络基于随机参数下求解7天SIRD模型生成的数据库构建,从而让网络从SIRD模型解中学习参数。最后,利用该集成模型从罗马尼亚COVID-19真实数据中获取参数估计值,并展示了10至45天不同时间跨度内死亡人数的预测结果。本研究的主要目标是将该方法应用于罗马尼亚COVID-19疫情演变分析,但也在匈牙利、捷克共和国和波兰等其他国家的案例中得到了类似结果。理论定理保证了从报告数据中恢复模型参数的可行性。我们认为该方法可作为处理传染病短期预测或其他仓室模型的通用工具。