{"title":"GLOBAL DYNAMICS AND OPTIMAL CONTROL FOR A VECTOR-BORNE EPIDEMIC MODEL WITH MULTI-CLASS-AGE STRUCTURE AND HORIZONTAL TRANSMISSION","authors":"Shuangshuang Liang, Shengfu Wang, Lin Hu, L. Nie","doi":"10.1142/s0218339023500109","DOIUrl":null,"url":null,"abstract":"An age-structured vector-borne disease model with horizontal transmission is proposed and studied in this paper, where the incubation ages of both host and vector and the immunity age of host are also introduced to consider the effects of multi-class-age structure. The reproductive number [Formula: see text] is derived as a threshold value to determine the existence and stability of the disease-free and endemic steady states. Furthermore, by constructing suitable Lyapunov functionals, the global threshold dynamics of this model is established by [Formula: see text], that is, the disease-free equilibrium is globally asymptotically stable when [Formula: see text], while if [Formula: see text] the endemic equilibrium is globally asymptotically stable. In addition, considering the limited budget of the centers for disease control and prevention (CDC) in the process of disease control, we present an optimal control problem with a fixed total expenditure, and discuss the existence of the most control strategy for this disease. Finally, some numerical simulations are performed to support the theoretical results.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-31","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/s0218339023500109","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
An age-structured vector-borne disease model with horizontal transmission is proposed and studied in this paper, where the incubation ages of both host and vector and the immunity age of host are also introduced to consider the effects of multi-class-age structure. The reproductive number [Formula: see text] is derived as a threshold value to determine the existence and stability of the disease-free and endemic steady states. Furthermore, by constructing suitable Lyapunov functionals, the global threshold dynamics of this model is established by [Formula: see text], that is, the disease-free equilibrium is globally asymptotically stable when [Formula: see text], while if [Formula: see text] the endemic equilibrium is globally asymptotically stable. In addition, considering the limited budget of the centers for disease control and prevention (CDC) in the process of disease control, we present an optimal control problem with a fixed total expenditure, and discuss the existence of the most control strategy for this disease. Finally, some numerical simulations are performed to support the theoretical results.
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.