Bilge Ayse Humeyra, Samanlioglu Funda, Ergonul Onder
Department of Industrial Engineering, Faculty of Engineering and Natural Sciences, Kadir Has University, Istanbul, Turkey,
J Math Biol. 2015 Oct;71(4):767-94. doi: 10.1007/s00285-014-0838-z. Epub 2014 Oct 14.
The susceptible-infected-removed (SIR) and the susceptible-exposed-infected-removed (SEIR) epidemic models with constant parameters are adequate for describing the time evolution of seasonal diseases for which available data usually consist of fatality reports. The problems associated with the determination of system parameters starts with the inference of the number of removed individuals from fatality data, because the infection to death period may depend on health care factors. Then, one encounters numerical sensitivity problems for the determination of the system parameters from a correct but noisy representative of the number of removed individuals. Finally as the available data is necessarily a normalized one, the models fitting this data may not be unique. We prove that the parameters of the (SEIR) model cannot be determined from the knowledge of a normalized curve of "Removed" individuals and we show that the proportion of removed individuals, [Formula: see text], is invariant under the interchange of the incubation and infection periods and corresponding scalings of the contact rate. On the other hand we prove that the SIR model fitting a normalized curve of removed individuals is unique and we give an implicit relation for the system parameters in terms of the values of [Formula: see text] and [Formula: see text], where [Formula: see text] is the steady state value of [Formula: see text] and [Formula: see text] and [Formula: see text] are the values of [Formula: see text] and its derivative at the inflection point [Formula: see text] of [Formula: see text]. We use these implicit relations to provide a robust method for the estimation of the system parameters and we apply this procedure to the fatality data for the H1N1 epidemic in the Czech Republic during 2009. We finally discuss the inference of the number of removed individuals from observational data, using a clinical survey conducted at major hospitals in Istanbul, Turkey, during 2009 H1N1 epidemic.
具有恒定参数的易感-感染-移除（SIR）和易感-暴露-感染-移除（SEIR）流行病模型足以描述季节性疾病的时间演变，对于这类疾病，可用数据通常包括死亡报告。与系统参数确定相关的问题始于从死亡数据推断移除个体的数量，因为感染到死亡的时间可能取决于医疗保健因素。然后，从正确但有噪声的移除个体数量代表中确定系统参数时会遇到数值敏感性问题。最后，由于可用数据必然是归一化的数据，拟合此数据的模型可能不是唯一的。我们证明，无法从“移除”个体的归一化曲线的知识中确定（SEIR）模型的参数，并且我们表明，移除个体的比例[公式：见原文]在潜伏期和感染期互换以及接触率相应缩放的情况下是不变的。另一方面，我们证明拟合移除个体归一化曲线的SIR模型是唯一的，并且我们根据[公式：见原文]和[公式：见原文]的值给出系统参数的隐式关系，其中[公式：见原文]是[公式：见原文]的稳态值，[公式：见原文]和[公式：见原文]是[公式：见原文]在[公式：见原文]的拐点[公式：见原文]处及其导数的值。我们使用这些隐式关系提供一种稳健的系统参数估计方法，并将此过程应用于2009年捷克共和国H1N1疫情的死亡数据。最后，我们利用2009年H1N1疫情期间在土耳其伊斯坦布尔主要医院进行的临床调查，讨论从观测数据推断移除个体数量的问题。
