{"title":"年龄组爵士模型的分析特性和数值保存:应用于信息扩散","authors":"A. Cardone, Patricia Diaz de Alba, B. Paternoster","doi":"10.1115/1.4065437","DOIUrl":null,"url":null,"abstract":"\n This paper analyzes an age-group SIR (Susceptible-Infected-Recovered) model. Theoretical results concerning the conservation of the total population, the positivity of the analytical solution, and the final size of the epidemic are derived. Since the model is a nonlinear system of ordinary differential equations, a numerical approximation is considered, based on Standard and non Standard Finite Difference methods, and on the Modified Patankar Euler method. The numerical preservation of the qualitative properties of the analytical solution is studied. The obtained results are applied to the diffusion of information in social networks. The effectiveness of the different numerical approaches is shown through several numerical tests on real data.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytical Properties and Numerical Preservation of an Age-Group Sir Model: Application to the Diffusion of Information\",\"authors\":\"A. Cardone, Patricia Diaz de Alba, B. Paternoster\",\"doi\":\"10.1115/1.4065437\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n This paper analyzes an age-group SIR (Susceptible-Infected-Recovered) model. Theoretical results concerning the conservation of the total population, the positivity of the analytical solution, and the final size of the epidemic are derived. Since the model is a nonlinear system of ordinary differential equations, a numerical approximation is considered, based on Standard and non Standard Finite Difference methods, and on the Modified Patankar Euler method. The numerical preservation of the qualitative properties of the analytical solution is studied. The obtained results are applied to the diffusion of information in social networks. The effectiveness of the different numerical approaches is shown through several numerical tests on real data.\",\"PeriodicalId\":54858,\"journal\":{\"name\":\"Journal of Computational and Nonlinear Dynamics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Nonlinear Dynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4065437\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Nonlinear Dynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4065437","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Analytical Properties and Numerical Preservation of an Age-Group Sir Model: Application to the Diffusion of Information
This paper analyzes an age-group SIR (Susceptible-Infected-Recovered) model. Theoretical results concerning the conservation of the total population, the positivity of the analytical solution, and the final size of the epidemic are derived. Since the model is a nonlinear system of ordinary differential equations, a numerical approximation is considered, based on Standard and non Standard Finite Difference methods, and on the Modified Patankar Euler method. The numerical preservation of the qualitative properties of the analytical solution is studied. The obtained results are applied to the diffusion of information in social networks. The effectiveness of the different numerical approaches is shown through several numerical tests on real data.
期刊介绍:
The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.