{"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":"<p>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 ℜ<sub>0</sub> > 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.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"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\":\"<p>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 ℜ<sub>0</sub> > 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.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2022-01-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mma.8088\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.8088","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","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。
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.
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