Application of neural-network hybrid models in estimating the infection functions of nonlinear epidemic models  

作　　者：Chentong Li Changsheng Zhou Junmin Liu Yao Rong 

机构地区：[1]Guangdong Key Laboratory of Modern Control Technology Institute of Intelligent Manufacturing Guangdong Academy of Science Guangzhou,Guangdong 510070,P.R.China [2]School of Mathematics and Information Science Guangzhou University,Guangzhou Guangdong 510006,P.R.China [3]School of Mathematics and Statistics Xi'an Jiaotong University Xi'an,Shaanxi 710049,P.R.China [4]College of Engineering Physics Shenzhen Technology University Shenzhen,Guangdong 518118,P.R.China

出　　处：《International Journal of Biomathematics》2024年第6期141-159,共19页生物数学学报(英文版)

基　　金：This work was funded by the GDAS'Project of Science and Technology Development(2021GDASYL-20210103089);Postdoctoral Research Foundation of China(2021M690747);National Natural Science Foundation of China(12001139,61877049 and 11991023);Science and Technology Program of Guangzhou(202007040007);GDAS'Project of Science and Technology Development(2019GDASYL-0502007);Guangdong Provincial Rural Revitalization Strategy Special Fund Project(2019KJ138);Guangdong Basic and Applied Basic Research Foundation(2019A1515110503).

摘　　要：Hybrid neural network models are effective in analyzing time-series data by combining the strengths of neural networks and differential equation models.Although most studies have focused on linear hybrid models,few have examined nonlinear problems.This work explores the potential of a hybrid nonlinear epidemic neural network in predicting the correct infection function of an epidemic model.We design a novel loss function by combining bifurcation theory and mean-squared error loss to ensure the trainability of the hybrid model.Additionally,we identify unique existence conditions that support ordinary differential equations for estimating the correct infection function.Moreover,numerical experiments using the Runge-Kutta method confirm our proposed model's soundness both on our synthetic data and the real COVID-19 data.

关 键 词：Differential equations epidemic model hybrid model neural network 

分 类 号：O17[理学—数学]