论文标题
SIR流行模型的分析参数估计。申请COVID-19大流行
Analytical parameter estimation of the SIR epidemic model. Applications to the COVID-19 pandemic
论文作者
论文摘要
2019年冠状病毒病（COVID-19）大流行病及其持续进展的戏剧性爆发增强了科学界对流行性建模和预测的兴趣。 SIR（易感性感染的）模型是一个简单的流行病爆发数学模型，但是数十年来，它避免了社区推导明确解决方案的努力。目前的工作表明，这是一项非平凡的任务。值得注意的是，已证明该模型的明确解决方案需要引入与Wright的Omega功能有关的新的先验特殊功能。本手稿报告了适用于SIR模型参数估计的新分析结果和数值例程。手稿引入了近似发生率变量的迭代算法，从而可以从观察到的病例数中估算模型参数。在2020年1月至2020年6月，欧洲疾病预防与控制中心（ECDC）的数据为数值方法举例说明了。
The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modeling and forecasting. The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the community to derive an explicit solution. The present work demonstrates that this is a non-trivial task. Notably, it is proven that the explicit solution of the model requires the introduction of a new transcendental special function, related to the Wright's Omega function. The present manuscript reports new analytical results and numerical routines suitable for parametric estimation of the SIR model. The manuscript introduces iterative algorithms approximating the incidence variable, which allows for estimation of the model parameters from the numbers of observed cases. The numerical approach is exemplified with data from the European Centre for Disease Prevention and Control (ECDC) for several European countries in the period Jan 2020 -- Jun 2020.
