基于改进的随机SEIR模型分析传染病的控制再生数

Analysis of the Controlled Regeneration Number of Infectious Diseases Based on an Improved Stochastic SEIR Model

摘要: 目的：为了研究传染病的变化特征，提出了改进的随机SEIR模型去仿真疫情的变化。方法：该模型针对仅考虑隔离新增感染患者的模型，增加了对原本存在的潜伏者的隔离行为，完善了这个模型。并且为了可以更好地对疫情变化做出精确的模拟，在求模型参数时使用决策树对疫情过程分段，使得仿真更贴合疫情的变化过程。最后利用最小二乘法计算出参数，得到各个阶段的控制再生数。结果：在验证的部分，对随机SEIR模型进行社区核酸阳性人数HE和隔离人群核酸阳性人数HEq的精确值求解，并将其与实际数据对比，结果显示，改进随机SEIR模型可以较好地反映疫情变化。结论：疫情大概在四十天的时候开始走到拐点，而且这时期之后的控制再生数基本都小于1。通过观察控制再生数计算公式，可以发现主要是隔离率P的上升使得控制再生数小于1，所以后期疫情得到控制的原因主要是隔离率P的上升。

Abstract: Objective: In order to study the changing characteristics of the epidemic, an improved stochastic SEIR model was proposed to simulate the changes of the epidemic. Methods: The improved model adds the isolation behavior of pre-existing latent people to the original model that only considers the isolation of newly infected patients. In order to better simulate the changes of the epidemic, the decision tree is used to segment the epidemic process when finding the model parameters, so that the simulation is more in line with the change process of the epidemic. Finally, the parameters cal-culated by the least squares method are used to find the controlled regeneration number for each stage. Results: In the verification part, the random SEIR model was solved for the exact values of the number of nucleic acid positive people HE in the community and the number of nucleic acid positive people in the isolated population HEq, and compared them with the actual data, and the results showed that the random SEIR model with improved could better reflect the changes of the epidem-ic. Conclusions: The epidemic began to reach an inflection point at about forty days, and the number of controlled regeneration after this period was basically less than 1. By observing the calculation formula of the controlled regeneration number, it can be found that the increase of the isolation rate P makes the controlled regeneration number less than 1, so the reason for the control of the epidemic in the later stage is mainly the increase of the isolation rate P.