{"title":"异构网络上随机 SIR 流行病最终规模的渐近分布","authors":"Xiaojie Jing , Guirong Liu , Zhen Jin","doi":"10.1016/j.aml.2024.109317","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, a Markovian SIR model on a heterogeneous network is considered. The law of large numbers and the central limit theorem of the epidemic process in a large population are provided. Further, the asymptotic distribution of the final size is given. Finally, by numerical and stochastic simulations, it is clear to show that our method performs well in approximation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109317"},"PeriodicalIF":2.9000,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic distribution of the final size of a stochastic SIR epidemic on heterogeneous networks\",\"authors\":\"Xiaojie Jing , Guirong Liu , Zhen Jin\",\"doi\":\"10.1016/j.aml.2024.109317\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, a Markovian SIR model on a heterogeneous network is considered. The law of large numbers and the central limit theorem of the epidemic process in a large population are provided. Further, the asymptotic distribution of the final size is given. Finally, by numerical and stochastic simulations, it is clear to show that our method performs well in approximation.</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"160 \",\"pages\":\"Article 109317\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965924003379\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924003379","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
本文考虑了异构网络上的马尔可夫 SIR 模型。本文提供了大数定律和大群体中流行过程的中心极限定理。此外，还给出了最终规模的渐近分布。最后，通过数值模拟和随机模拟，可以清楚地看到我们的方法在近似方面表现良好。
Asymptotic distribution of the final size of a stochastic SIR epidemic on heterogeneous networks
In this paper, a Markovian SIR model on a heterogeneous network is considered. The law of large numbers and the central limit theorem of the epidemic process in a large population are provided. Further, the asymptotic distribution of the final size is given. Finally, by numerical and stochastic simulations, it is clear to show that our method performs well in approximation.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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