摘要
目的由于传染病的不断复杂化,一类传播过程中出现大量隐性感染人群的疾病逐渐流行,提出一种基于SEIR模型改进后的SEIR-A模型来更加准确地刻画该类疾病的传播机制。方法在动力学模型方面,主要有以下两点改进:一是假设潜伏期人群和显性感染人群具有一致的传染因子;二是引入具有不同传染性的隐性感染人群A,且增添隐性感染者向显性感染者单向转换的常值因子ω,构建一类具有特殊隐性感染人群的SEIR-A模型。此外,将改进后的SEIR-A模型与时间卷积网络TCN模型线性结合,得到一种动力学模型和深度学习模型相互融合的混合模型。结果通过真实数据的拟合,结果表明:SEIR-A模型可以模拟传染病的总体趋势,且能够对该疾病中现存隐性感染人群和累计恢复人群做出准确拟合,决定系数R^(2)分别达到0.9870和0.9899,证明该模型合理;SEIR-A与TCN的混合模型可以实现对复杂现存显性感染人群的拟合,相较于单一的SEIR-A模型、TCN和LSTM模型,该混合模型的决定系数R^(2)达到了0.9611,取得了5种对比模型中最优的拟合精度。结论传统动力学和深度学习的结合,可以在体现疾病传播机理的同时有效解决传统模型拟合精度不高的问题,对传染病研究具有现实意义。
Objective A modified SEIR-A model based on the SEIR model was proposed to describe the transmission mechanism of infectious diseases more accurately,in view of the increasing complexity of infectious diseases and the gradual prevalence of a kind of diseases with a large number of latent infections in the process of transmission.Methods In terms of the kinetic model,there were two main improvements.One was to assume that the incubation period population and the dominant infected population had the same infectious factors;the other was to introduce a recessive infection population A with different infectiousness,and add a constant factorωfor one-way conversion from recessive infection to dominant infection,so as to construct an SEIR-A model of a special recessive infection population.In addition,the improved SEIR-A model was linearly combined with the TCN model of time convolution network,and a hybrid model with the fusion of dynamic model and deep learning model was obtained.Results Through the fitting of real data,the results showed that the SEIR-A model could simulate the general trend of infectious diseases,and could accurately fit the existing recessive infected population and the accumulated recovered population in the disease,and the determination coefficient R^(2)reached 0.9870 and 0.9899,respectively,proving that the model was reasonable.The hybrid model of SEIR-A and TCN can fit the complex existing dominant infected population.Compared with the single SEIR-A model,TCN model and LSTM model,the determination coefficient R^(2)of the hybrid model reached 0.9611,obtaining the best fitting accuracy among the five comparative models.Conclusion The combination of traditional dynamics and deep learning can effectively solve the problem of low fitting accuracy of traditional models while embodying the mechanism of disease transmission,which has practical significance for the study of infectious diseases.
作者
李季
乔敏
邹黎敏
LI Ji;QIAO Min;ZOU Limin(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China)
出处
《重庆工商大学学报（自然科学版）》
2023年第6期83-92,共10页
Journal of Chongqing Technology and Business University:Natural Science Edition
基金
重庆市教育委员会项目(KJQN202000816).
