{"title":"STABILITY ANALYSIS AND OPTIMAL CONTROL OF A LYME DISEASE MODEL WITH INSECTICIDES SPRAYING AND VACCINATION","authors":"Bei Sun, K. Okosun, Xue Zhang","doi":"10.1142/s021833902250022x","DOIUrl":null,"url":null,"abstract":"This paper studies an SIS-type Lyme transmission model incorporating insecticides spraying and vaccination as interventions. We obtain the positivity and boundedness of solutions, calculate the basic reproduction number, and discuss the global stability of disease-free and endemic equilibria when the basic reproduction number [Formula: see text] and [Formula: see text], respectively. We apply Pontryagin’s maximum principle to explore an optimal control strategy to minimize the number of infected ticks and hosts and the cost of using insecticides and vaccination. We design numerical simulations to illustrate the effectiveness of theoretical analysis.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Biological Systems","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1142/s021833902250022x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BIOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
This paper studies an SIS-type Lyme transmission model incorporating insecticides spraying and vaccination as interventions. We obtain the positivity and boundedness of solutions, calculate the basic reproduction number, and discuss the global stability of disease-free and endemic equilibria when the basic reproduction number [Formula: see text] and [Formula: see text], respectively. We apply Pontryagin’s maximum principle to explore an optimal control strategy to minimize the number of infected ticks and hosts and the cost of using insecticides and vaccination. We design numerical simulations to illustrate the effectiveness of theoretical analysis.
期刊介绍：
The Journal of Biological Systems is published quarterly. The goal of the Journal is to promote interdisciplinary approaches in Biology and in Medicine, and the study of biological situations with a variety of tools, including mathematical and general systems methods. The Journal solicits original research papers and survey articles in areas that include (but are not limited to):
Complex systems studies; isomorphies; nonlinear dynamics; entropy; mathematical tools and systems theories with applications in Biology and Medicine.
Interdisciplinary approaches in Biology and Medicine; transfer of methods from one discipline to another; integration of biological levels, from atomic to molecular, macromolecular, cellular, and organic levels; animal biology; plant biology.
Environmental studies; relationships between individuals, populations, communities and ecosystems; bioeconomics, management of renewable resources; hierarchy theory; integration of spatial and time scales.
Evolutionary biology; co-evolutions; genetics and evolution; branching processes and phyllotaxis.
Medical systems; physiology; cardiac modeling; computer models in Medicine; cancer research; epidemiology.
Numerical simulations and computations; numerical study and analysis of biological data.
Epistemology; history of science.
The journal will also publish book reviews.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
