一类SEIRS模型的全局渐近稳定性及其非标准有限差分格式解

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-01-01 DOI:10.23952/jnfa.2020.34

M. T. Hoang, O. Egbelowo

{"title":"一类SEIRS模型的全局渐近稳定性及其非标准有限差分格式解","authors":"M. T. Hoang, O. Egbelowo","doi":"10.23952/jnfa.2020.34","DOIUrl":null,"url":null,"abstract":". In this paper, we present a mathematically rigorous analysis for the global asymptotic stability of a recognized SEIRS model with nonlinear incidence and vertical transmission. Our main objective is to re-establish the local asymptotic stability of the disease endemic equilibrium point without the assumption proposed in [L. Qi, J. Cui, The stability of an SEIRS model with nonlinear incidence, vertical transmission and time delay, Appl. Math. Comput. 221 (2013), 360-366] and prove that this equilibrium point is not only locally asymptotically stable but also globally asymptotically stable if it exists. Therefore, the global stability of the model is established rigorously. Additionally, we design nonstandard ﬁnite difference (NSFD) schemes that preserve essential properties of the SEIRS model using the Mickens methodology. A set of numerical experiments are performed to support the validity of the theoretical results as well as to show advantages and efﬁciency of the NSFD schemes over the standard ﬁnite difference schemes.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global asymptotic stability of an SEIRS model and its solutions by nonstandard finite difference schemes\",\"authors\":\"M. T. Hoang, O. Egbelowo\",\"doi\":\"10.23952/jnfa.2020.34\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper, we present a mathematically rigorous analysis for the global asymptotic stability of a recognized SEIRS model with nonlinear incidence and vertical transmission. Our main objective is to re-establish the local asymptotic stability of the disease endemic equilibrium point without the assumption proposed in [L. Qi, J. Cui, The stability of an SEIRS model with nonlinear incidence, vertical transmission and time delay, Appl. Math. Comput. 221 (2013), 360-366] and prove that this equilibrium point is not only locally asymptotically stable but also globally asymptotically stable if it exists. Therefore, the global stability of the model is established rigorously. Additionally, we design nonstandard ﬁnite difference (NSFD) schemes that preserve essential properties of the SEIRS model using the Mickens methodology. A set of numerical experiments are performed to support the validity of the theoretical results as well as to show advantages and efﬁciency of the NSFD schemes over the standard ﬁnite difference schemes.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23952/jnfa.2020.34\",\"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":"1085","ListUrlMain":"https://doi.org/10.23952/jnfa.2020.34","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

．本文对一类具有非线性入射和垂直传输的公认SEIRS模型的全局渐近稳定性进行了严密的数学分析。我们的主要目标是在不采用[L]中提出的假设的情况下，重新建立疾病地方性平衡点的局部渐近稳定性。齐军，崔军，具有非线性入射、垂直传输和时间延迟的SEIRS模型的稳定性，应用科学。数学。计算[j] . 221(2013)， 360-366]，证明该平衡点存在时不仅局部渐近稳定，而且全局渐近稳定。因此，严格地建立了模型的全局稳定性。此外，我们设计了非标准有限差分(NSFD)方案，使用Mickens方法保留了SEIRS模型的基本属性。通过一组数值实验验证了理论结果的有效性，并证明了NSFD格式相对于标准有限差分格式的优势和效率。

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

Global asymptotic stability of an SEIRS model and its solutions by nonstandard finite difference schemes

. In this paper, we present a mathematically rigorous analysis for the global asymptotic stability of a recognized SEIRS model with nonlinear incidence and vertical transmission. Our main objective is to re-establish the local asymptotic stability of the disease endemic equilibrium point without the assumption proposed in [L. Qi, J. Cui, The stability of an SEIRS model with nonlinear incidence, vertical transmission and time delay, Appl. Math. Comput. 221 (2013), 360-366] and prove that this equilibrium point is not only locally asymptotically stable but also globally asymptotically stable if it exists. Therefore, the global stability of the model is established rigorously. Additionally, we design nonstandard ﬁnite difference (NSFD) schemes that preserve essential properties of the SEIRS model using the Mickens methodology. A set of numerical experiments are performed to support the validity of the theoretical results as well as to show advantages and efﬁciency of the NSFD schemes over the standard ﬁnite difference schemes.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.