年龄结构结核复发传播模型的全局稳定性

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2022-01-05 DOI:10.1002/mma.8088

Lili Liu, Jian Zhang, Yazhi Li, Xianning Liu

{"title":"年龄结构结核复发传播模型的全局稳定性","authors":"Lili Liu, Jian Zhang, Yazhi Li, Xianning Liu","doi":"10.1002/mma.8088","DOIUrl":null,"url":null,"abstract":"We reconsider the model presented in Cao et al. (2020, doi:10.1002/mma.6156), where the global asymptotic stability (GAS) of the endemic steady state (ESS) was unresolved when ℜ0 > 1. We recompute the existence of ESS in detail, re-establish the GAS of the disease-free steady state (DFSS) in a simple and direct manner, and, furthermore, resolve the GAS of ESS, which was left as an open problem in the above paper. We adopt the method of Lyapunov functional with a key skill of selecting some novel appropriate kernel functions.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"45 9","pages":"5622-5630"},"PeriodicalIF":1.8000,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the global stability of an age-structured tuberculosis transmission model with relapse\",\"authors\":\"Lili Liu, Jian Zhang, Yazhi Li, Xianning Liu\",\"doi\":\"10.1002/mma.8088\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We reconsider the model presented in Cao et al. (2020, doi:10.1002/mma.6156), where the global asymptotic stability (GAS) of the endemic steady state (ESS) was unresolved when ℜ0 > 1. We recompute the existence of ESS in detail, re-establish the GAS of the disease-free steady state (DFSS) in a simple and direct manner, and, furthermore, resolve the GAS of ESS, which was left as an open problem in the above paper. We adopt the method of Lyapunov functional with a key skill of selecting some novel appropriate kernel functions.\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":\"45 9\",\"pages\":\"5622-5630\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2022-01-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods in the Applied Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mma.8088\",\"RegionNum\":3,\"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":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.8088","RegionNum":3,"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

我们重新考虑Cao et al. (2020, doi:10.1002/mma.6156)中提出的模型，其中地方性稳态(ESS)的全局渐近稳定性(GAS)在r0 > 1时无法解决。我们详细地重新计算了无病稳态的存在性，以一种简单直接的方式重新建立了无病稳态(DFSS)的GAS，并在此基础上解决了本文遗留的一个开放性问题——无病稳态GAS。我们采用李雅普诺夫泛函方法，关键技巧是选择一些新颖合适的核函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the global stability of an age-structured tuberculosis transmission model with relapse

We reconsider the model presented in Cao et al. (2020, doi:10.1002/mma.6156), where the global asymptotic stability (GAS) of the endemic steady state (ESS) was unresolved when ℜ₀ > 1. We recompute the existence of ESS in detail, re-establish the GAS of the disease-free steady state (DFSS) in a simple and direct manner, and, furthermore, resolve the GAS of ESS, which was left as an open problem in the above paper. We adopt the method of Lyapunov functional with a key skill of selecting some novel appropriate kernel functions.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.