{"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":1,"journal":{"name":"Accounts of Chemical Research","volume":"18 2","pages":""},"PeriodicalIF":16.4000,"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\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":\"18 2\",\"pages\":\"\"},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4065437\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4065437","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","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:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.