考虑气候变率的疟疾传播建模与最优控制分析

IF 0.9 Q3 MATHEMATICS, APPLIED Computational and Mathematical Methods Pub Date : 2022-12-02 DOI:10.1155/2022/9667396
Temesgen Duressa Keno, Lemessa Bedjisa Dano, Oluwole Daniel Makinde
{"title":"考虑气候变率的疟疾传播建模与最优控制分析","authors":"Temesgen Duressa Keno,&nbsp;Lemessa Bedjisa Dano,&nbsp;Oluwole Daniel Makinde","doi":"10.1155/2022/9667396","DOIUrl":null,"url":null,"abstract":"<div>\n <p>In this paper, we present a nonlinear deterministic mathematical model for malaria transmission dynamics incorporating climatic variability as a factor. First, we showed the limited region and nonnegativity of the solution, which demonstrate that the model is biologically relevant and mathematically well-posed. Furthermore, the fundamental reproduction number was determined using the next-generation matrix approach, and the sensitivity of model parameters was investigated to determine the most affecting parameter. The Jacobian matrix and the Lyapunov function are used to illustrate the local and global stability of the equilibrium locations. If the fundamental reproduction number is smaller than one, a disease-free equilibrium point is both locally and globally asymptotically stable, but endemic equilibrium occurs otherwise. The model exhibits forward and backward bifurcation. Moreover, we applied the optimal control theory to describe the optimal control model that incorporates three controls, namely, using treated bed net, treatment of infected with antimalaria drugs, and indoor residual spraying strategy. The Pontryagin’s maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the numerical simulation of optimality system and cost-effectiveness analysis reveals that the combination of treated bed net and treatment is the most optimal and least-cost strategy to minimize the malaria.</p>\n </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/9667396","citationCount":"0","resultStr":"{\"title\":\"Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability\",\"authors\":\"Temesgen Duressa Keno,&nbsp;Lemessa Bedjisa Dano,&nbsp;Oluwole Daniel Makinde\",\"doi\":\"10.1155/2022/9667396\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n <p>In this paper, we present a nonlinear deterministic mathematical model for malaria transmission dynamics incorporating climatic variability as a factor. First, we showed the limited region and nonnegativity of the solution, which demonstrate that the model is biologically relevant and mathematically well-posed. Furthermore, the fundamental reproduction number was determined using the next-generation matrix approach, and the sensitivity of model parameters was investigated to determine the most affecting parameter. The Jacobian matrix and the Lyapunov function are used to illustrate the local and global stability of the equilibrium locations. If the fundamental reproduction number is smaller than one, a disease-free equilibrium point is both locally and globally asymptotically stable, but endemic equilibrium occurs otherwise. The model exhibits forward and backward bifurcation. Moreover, we applied the optimal control theory to describe the optimal control model that incorporates three controls, namely, using treated bed net, treatment of infected with antimalaria drugs, and indoor residual spraying strategy. The Pontryagin’s maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the numerical simulation of optimality system and cost-effectiveness analysis reveals that the combination of treated bed net and treatment is the most optimal and least-cost strategy to minimize the malaria.</p>\\n </div>\",\"PeriodicalId\":100308,\"journal\":{\"name\":\"Computational and Mathematical Methods\",\"volume\":\"2022 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-12-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/9667396\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational and Mathematical Methods\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1155/2022/9667396\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Mathematical Methods","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1155/2022/9667396","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

摘要

在本文中,我们提出了一个非线性确定性数学模型疟疾传播动力学纳入气候变化作为一个因素。首先,我们展示了解的有限区域和非负性,这表明该模型具有生物学相关性和数学上的良好定姿。采用新一代矩阵法确定了基本再现数,并研究了模型参数的灵敏度,确定了影响最大的参数。利用雅可比矩阵和李雅普诺夫函数说明平衡位置的局部稳定性和全局稳定性。如果基本繁殖数小于1,则无病平衡点是局部和全局渐近稳定的,否则发生地方性平衡。该模型具有正向分岔和后向分岔。此外,我们应用最优控制理论描述了包含三个控制的最优控制模型,即使用处理过的蚊帐、使用抗疟药物治疗感染者和室内残留喷洒策略。引入庞特里亚金极大值原理,得到了最优控制问题的必要条件。最后,通过优化系统的数值模拟和成本-效果分析表明,处理过的蚊帐与治疗相结合是减少疟疾的最优、成本最小的策略。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

摘要图片

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

In this paper, we present a nonlinear deterministic mathematical model for malaria transmission dynamics incorporating climatic variability as a factor. First, we showed the limited region and nonnegativity of the solution, which demonstrate that the model is biologically relevant and mathematically well-posed. Furthermore, the fundamental reproduction number was determined using the next-generation matrix approach, and the sensitivity of model parameters was investigated to determine the most affecting parameter. The Jacobian matrix and the Lyapunov function are used to illustrate the local and global stability of the equilibrium locations. If the fundamental reproduction number is smaller than one, a disease-free equilibrium point is both locally and globally asymptotically stable, but endemic equilibrium occurs otherwise. The model exhibits forward and backward bifurcation. Moreover, we applied the optimal control theory to describe the optimal control model that incorporates three controls, namely, using treated bed net, treatment of infected with antimalaria drugs, and indoor residual spraying strategy. The Pontryagin’s maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the numerical simulation of optimality system and cost-effectiveness analysis reveals that the combination of treated bed net and treatment is the most optimal and least-cost strategy to minimize the malaria.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
2.20
自引率
0.00%
发文量
0
期刊最新文献
On the Efficiency of the Newly Developed Composite Randomized Response Technique Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method A Mathematical Analysis of the Impact of Immature Mosquitoes on the Transmission Dynamics of Malaria Parameter-Uniform Convergent Numerical Approach for Time-Fractional Singularly Perturbed Partial Differential Equations With Large Time Delay Mortality Prediction in COVID-19 Using Time Series and Machine Learning Techniques
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1