{"title":"Mathematical analysis of a non-convex optimal control problem for age-structured mosquito populations","authors":"Cícero Alfredo da Silva Filho, José Luiz Boldrini","doi":"10.1002/mma.10389","DOIUrl":null,"url":null,"abstract":"<p>We present a rigorous mathematical analysis of a non-convex optimal control problem for mosquito populations. The nonlinear model for the dynamics of the mosquito population takes in consideration the iterations among the immature (aquatic) subpopulation, the adult winged subpopulation, and the environment resources; the immature subpopulation is assumed to be age-structured. Moreover, the action of certain control mechanisms on these subpopulations is also taken in account. The cost functional to be minimized is non-convex. The proof of the existence of an optimal control is done by using fixed point arguments and a special minimizing sequence obtained with the help of Ekeland's variational principle.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1381-1410"},"PeriodicalIF":1.8000,"publicationDate":"2024-08-06","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.10389","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
Abstract
We present a rigorous mathematical analysis of a non-convex optimal control problem for mosquito populations. The nonlinear model for the dynamics of the mosquito population takes in consideration the iterations among the immature (aquatic) subpopulation, the adult winged subpopulation, and the environment resources; the immature subpopulation is assumed to be age-structured. Moreover, the action of certain control mechanisms on these subpopulations is also taken in account. The cost functional to be minimized is non-convex. The proof of the existence of an optimal control is done by using fixed point arguments and a special minimizing sequence obtained with the help of Ekeland's variational principle.
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.
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