论文标题
SIR等平均场理论的应用和扩展讨论Covid-19的非均值现场问题
Application and Extension of Mean-Field Theory such as SIR to Discuss the Non-Mean Field Problem of COVID-19
论文作者
论文摘要
有效的感染机会人群(EIOP)的概念已纳入SIQR模型,并假定该EIOP会随着感染的传播而改变,这被称为有效的SIQR模型。当用该模型计算时,未感染的种群S随时间流逝而减小。但是,当EIOP N由于任何原因而增加时,感染阈值就大于1。即使在第一波似乎已经消失后,感染也开始再次扩散。首先,我们发现EIOP的曲线变化,因此该模型产生的计算与第一波和第二波的数据匹配。然后,我们使用此曲线仅与仅第二波的数据拟合,并预测第三波。在新的冠状病毒感染的情况下,对数据收集有各种限制,以识别数学模型的各个系数,而真实值几乎是未知的。因此,本文中的讨论仅与预测计算的数据拟合有关。因此,对真实值的模拟不是针对的。但是,由于受感染者的数据反映了真实价值,因此数据拟合的结果可用于预测感染者,孤立的护理接收者,住院患者和严重患者。它们对于对感染的定性理解很有用。 EIOP的概念在连接均值场和非均值领域的意义上很重要,但是数据的存在至关重要,仅理论就无法模拟非均值领域。我们开发了两种方法来处理我们没有足够数据的非均值现场案例。我们已经简要介绍了它们。
The concept of the effective infection opportunity population (EIOP) was incorporated into the SIQR model, and it was assumed that this EIOP would change with the spread of infection, and this was named as the effective SIQR model. When calculated with this model, the uninfected population S decreases with the passage of time. However, when the EIOP N increases because of any reason, the infection threshold becomes larger than 1. Even after the first wave seems to have subsided, the infection begins to spread again. Firstly, we find the curve of EIOP change so that the calculation result by this model matches the data of the first and second waves. Then, we use this curve to fit with only the data of the second wave alone, and the third wave is predicted. In the case of new coronavirus infection, there are various restrictions on data collection to identify individual coefficients of mathematical models, and the true value is almost unknown. Therefore, the discussion in this paper is only about data fitting for predictive calculation. Therefore, the simulation on the true value is not aimed. However, since the data of infected persons reflect the true values, the results of data fitting can be used for the prediction of infected persons, isolated care recipients, inpatients, and severely ill persons. They are useful for a qualitative understanding of infection. The idea of EIOP is important in the sense that it connects the mean-field and the non-mean field, but the existence of data is essential, and the theory alone cannot simulate the non-mean field. We have developed two methods for treating the non-mean field cases where we don't have enough data. We have briefly introduced them.