M. A. El Yamani, Jaafar El Karkri, S. Lazaar, R. Aboulaich
{"title":"两组流行病学模型:稳定性分析及神经网络数值模拟","authors":"M. A. El Yamani, Jaafar El Karkri, S. Lazaar, R. Aboulaich","doi":"10.1142/s1793962323500290","DOIUrl":null,"url":null,"abstract":"This work has two principal goals. First, we investigate the asymptotic behavior of a two-group epidemiological model and determine the expression of its basic reproduction number using the dynamical systems approach based on the spectral radius of the relative matrix. Second, we simulate the obtained analytical results using a new deep learning method that associates the ordinary differential equations governing the model to neural networks. A general disease-free equilibrium is considered and sufficient conditions of stability and convergence are formulated. A detailed description of the neural network model used in the simulation is provided. Moreover, the proposed deep learning simulation algorithm is compared to the simulation provided by \"odeint\", a function from \"SciPy\" which is a Python library of mathematical routines.","PeriodicalId":45889,"journal":{"name":"International Journal of Modeling Simulation and Scientific Computing","volume":"33 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A two-group epidemiological model: Stability analysis and numerical simulation using neural network\",\"authors\":\"M. A. El Yamani, Jaafar El Karkri, S. Lazaar, R. Aboulaich\",\"doi\":\"10.1142/s1793962323500290\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work has two principal goals. First, we investigate the asymptotic behavior of a two-group epidemiological model and determine the expression of its basic reproduction number using the dynamical systems approach based on the spectral radius of the relative matrix. Second, we simulate the obtained analytical results using a new deep learning method that associates the ordinary differential equations governing the model to neural networks. A general disease-free equilibrium is considered and sufficient conditions of stability and convergence are formulated. A detailed description of the neural network model used in the simulation is provided. Moreover, the proposed deep learning simulation algorithm is compared to the simulation provided by \\\"odeint\\\", a function from \\\"SciPy\\\" which is a Python library of mathematical routines.\",\"PeriodicalId\":45889,\"journal\":{\"name\":\"International Journal of Modeling Simulation and Scientific Computing\",\"volume\":\"33 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Modeling Simulation and Scientific Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793962323500290\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Modeling Simulation and Scientific Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s1793962323500290","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
A two-group epidemiological model: Stability analysis and numerical simulation using neural network
This work has two principal goals. First, we investigate the asymptotic behavior of a two-group epidemiological model and determine the expression of its basic reproduction number using the dynamical systems approach based on the spectral radius of the relative matrix. Second, we simulate the obtained analytical results using a new deep learning method that associates the ordinary differential equations governing the model to neural networks. A general disease-free equilibrium is considered and sufficient conditions of stability and convergence are formulated. A detailed description of the neural network model used in the simulation is provided. Moreover, the proposed deep learning simulation algorithm is compared to the simulation provided by "odeint", a function from "SciPy" which is a Python library of mathematical routines.