{"title":"DYNAMICAL ANALYSIS OF TB MODEL WITH NONLINEAR INCIDENCE RATE AND OPTIMAL CONTROL","authors":"Shuping Li, Huafang Liu","doi":"10.1142/s0218339023500250","DOIUrl":null,"url":null,"abstract":"We propose and analyze a TB transmission model with nonlinear incidence rate, immunization and medical treatment. First, the existences and stabilities of the equilibrium are studied. The results indicate the basic reproduction number [Formula: see text] is the threshold of disease extinction and persistence. The disease-free equilibrium is globally asymptotically stable when [Formula: see text], and the disease will gradually disappear. The unique positive equilibrium is local stability and the disease is uniformly persistent when [Formula: see text]. Second, optimal control is added to the original model because of limited resources. Finally, the stability of the equilibrium and the theoretical results of optimal control are verified by numerical simulations, and the sensitivity of the parameters is analyzed by the PRCC method.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1142/s0218339023500250","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
Abstract
We propose and analyze a TB transmission model with nonlinear incidence rate, immunization and medical treatment. First, the existences and stabilities of the equilibrium are studied. The results indicate the basic reproduction number [Formula: see text] is the threshold of disease extinction and persistence. The disease-free equilibrium is globally asymptotically stable when [Formula: see text], and the disease will gradually disappear. The unique positive equilibrium is local stability and the disease is uniformly persistent when [Formula: see text]. Second, optimal control is added to the original model because of limited resources. Finally, the stability of the equilibrium and the theoretical results of optimal control are verified by numerical simulations, and the sensitivity of the parameters is analyzed by the PRCC method.
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.
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