{"title":"结核模型的最优控制分析","authors":"L. L. Obsu","doi":"10.1142/s0218339022500309","DOIUrl":null,"url":null,"abstract":"In this paper, an optimal control theory was applied to the tuberculosis (TB) model governed by system of nonlinear ordinary differential equations. The aim is to investigate the impact of treatment failure on the TB epidemic. An optimal control strategy is proposed to minimize the disease effect and cost incurred due to treatment failure. The existence and uniqueness of optimal controls are proved. The characterization of optimal paths is analytically derived using Pontryagin’s Minimum Principle. The control-induced model is then fitted using TB infected cases reported from the year 2010–2019 in East Shewa zone Oromia regional state, Ethiopia. Different simulation cases were performed to compare with analytical results. The simulation results show that the combined effect of awareness via various mass media and continuous supervision during the treatment period helps to reduce treatment failure and hence reduced the TB epidemic in the community.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"OPTIMAL CONTROL ANALYSIS OF A TUBERCULOSIS MODEL\",\"authors\":\"L. L. Obsu\",\"doi\":\"10.1142/s0218339022500309\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, an optimal control theory was applied to the tuberculosis (TB) model governed by system of nonlinear ordinary differential equations. The aim is to investigate the impact of treatment failure on the TB epidemic. An optimal control strategy is proposed to minimize the disease effect and cost incurred due to treatment failure. The existence and uniqueness of optimal controls are proved. The characterization of optimal paths is analytically derived using Pontryagin’s Minimum Principle. The control-induced model is then fitted using TB infected cases reported from the year 2010–2019 in East Shewa zone Oromia regional state, Ethiopia. Different simulation cases were performed to compare with analytical results. The simulation results show that the combined effect of awareness via various mass media and continuous supervision during the treatment period helps to reduce treatment failure and hence reduced the TB epidemic in the community.\",\"PeriodicalId\":54872,\"journal\":{\"name\":\"Journal of Biological Systems\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-10-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Biological Systems\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218339022500309\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"BIOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Biological Systems","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1142/s0218339022500309","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BIOLOGY","Score":null,"Total":0}
In this paper, an optimal control theory was applied to the tuberculosis (TB) model governed by system of nonlinear ordinary differential equations. The aim is to investigate the impact of treatment failure on the TB epidemic. An optimal control strategy is proposed to minimize the disease effect and cost incurred due to treatment failure. The existence and uniqueness of optimal controls are proved. The characterization of optimal paths is analytically derived using Pontryagin’s Minimum Principle. The control-induced model is then fitted using TB infected cases reported from the year 2010–2019 in East Shewa zone Oromia regional state, Ethiopia. Different simulation cases were performed to compare with analytical results. The simulation results show that the combined effect of awareness via various mass media and continuous supervision during the treatment period helps to reduce treatment failure and hence reduced the TB epidemic in the community.
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
