{"title":"具有检疫和标准发病率的流行病模型的均匀持续性新分析方法","authors":"Song-bai Guo, Yu-ling Xue, Xi-liang Li, Zuo-huan Zheng","doi":"10.1007/s10255-023-1078-y","DOIUrl":null,"url":null,"abstract":"<div><p>Inspired by the transmission characteristics of the Coronavirus disease 2019 (COVID-19), an epidemic model with quarantine and standard incidence rate is first developed, then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals, which means that the epidemic is uniformly persistent if the control reproduction number <span>\\({{\\cal R}_c} > 1\\)</span>. This approach can be applied to the related biomathematical models, and some existing works can be improved by using that. In addition, the infection-free equilibrium <i>V</i><sup>0</sup> of the model is locally asymptotically stable (LAS) if <span>\\({{\\cal R}_c} < 1\\)</span> and linearly stable if <span>\\({{\\cal R}_c} = 1\\)</span>; while <i>V</i><sup>0</sup> is unstable if <span>\\({{\\cal R}_c} > 1\\)</span>.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"695 - 707"},"PeriodicalIF":0.9000,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate\",\"authors\":\"Song-bai Guo, Yu-ling Xue, Xi-liang Li, Zuo-huan Zheng\",\"doi\":\"10.1007/s10255-023-1078-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Inspired by the transmission characteristics of the Coronavirus disease 2019 (COVID-19), an epidemic model with quarantine and standard incidence rate is first developed, then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals, which means that the epidemic is uniformly persistent if the control reproduction number <span>\\\\({{\\\\cal R}_c} > 1\\\\)</span>. This approach can be applied to the related biomathematical models, and some existing works can be improved by using that. In addition, the infection-free equilibrium <i>V</i><sup>0</sup> of the model is locally asymptotically stable (LAS) if <span>\\\\({{\\\\cal R}_c} < 1\\\\)</span> and linearly stable if <span>\\\\({{\\\\cal R}_c} = 1\\\\)</span>; while <i>V</i><sup>0</sup> is unstable if <span>\\\\({{\\\\cal R}_c} > 1\\\\)</span>.</p></div>\",\"PeriodicalId\":6951,\"journal\":{\"name\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"volume\":\"40 3\",\"pages\":\"695 - 707\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-05-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10255-023-1078-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-023-1078-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate
Inspired by the transmission characteristics of the Coronavirus disease 2019 (COVID-19), an epidemic model with quarantine and standard incidence rate is first developed, then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals, which means that the epidemic is uniformly persistent if the control reproduction number \({{\cal R}_c} > 1\). This approach can be applied to the related biomathematical models, and some existing works can be improved by using that. In addition, the infection-free equilibrium V0 of the model is locally asymptotically stable (LAS) if \({{\cal R}_c} < 1\) and linearly stable if \({{\cal R}_c} = 1\); while V0 is unstable if \({{\cal R}_c} > 1\).
期刊介绍:
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.