[1]郭中凯,任秋艳,李建生.具有年龄结构的SIR传染病模型的最优接种和治疗策略[J].南京师范大学学报(自然科学版),2019,42(01):28.[doi:10.3969/j.issn.1001-4616.2019.01.006]
　Guo Zhongkai,Ren Qiuyan,Li Jiansheng.Optimal Control of Age-Structured SIR Epidemic Modelwith Vaccination and Treatment[J].Journal of Nanjing Normal University(Natural Science Edition),2019,42(01):28.[doi:10.3969/j.issn.1001-4616.2019.01.006]
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具有年龄结构的SIR传染病模型的最优接种和治疗策略()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第42卷
期数:
2019年01期
页码:
28
栏目:
·数学·
出版日期:
2019-03-20

文章信息/Info

Title:
Optimal Control of Age-Structured SIR Epidemic Modelwith Vaccination and Treatment
文章编号:
1001-4616(2019)01-0028-08
作者:
郭中凯1; 2; 任秋艳1; 2; 李建生2
(1.兰州理工大学电气工程与信息工程学院,甘肃 兰州 730050)(2.兰州理工大学技术工程学院,甘肃 兰州 730050)
Author(s):
Guo Zhongkai1; 2; Ren Qiuyan1; 2; Li Jiansheng2
(1.College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 730050,China)(2.College of Technology and Engineering,Lanzhou University of Technology,Lanzhou 730050,China)
关键词:
年龄结构; 传染病; 最优控制; Ekeland变分原理
Keywords:
age-structured; epidemic; optimal control; Ekeland’s variational principle
分类号:
O157.13; Q141
DOI:
10.3969/j.issn.1001-4616.2019.01.006
文献标志码:
A
摘要:
研究了一类染病者具有年龄结构的SIR传染病模型的最优接种和治疗策略问题. 利用Banach压缩映射原理和Gronwall引理,证明了该传染病模型非负解的唯一性以及解对控制变量的连续依赖性. 借助切锥法锥技巧给出最优接种和治疗策略的必要条件. 根据Ekeland变分原理确立了最优接种和治疗策略的存在性和唯一性.
Abstract:
This article investigates an optimal control problem with vaccination and treatment for SIR epidemic model with age-structured infected. Uniqueness of non-negative solutions to the model and the continuous dependence of solution on control variables are proved by using the Banach contraction mapping principle and Gronwall’s lemma. Necessary optimality conditions of vaccination and treatment are derived by the use of tangent-normal cone technique. Existence of unique optimal control of vaccination and treatment is verified via Ekeland’s variational principle.

参考文献/References:

[1] 郭中凯,王文婷,李自珍. 具有脉冲免疫接种的SEIRS传染病模型分析[J]. 南京师大学报(自然科学版),2013,36(2):20-26.
[2]ZAMAN G,KANG Y H,CHO G,et al. Optimal strategy of vaccination and treatment in an SIR epidemic model[J]. Mathematics and computers in simulation,2017,136:63-77.
[3]廖书,杨炜明. 一类含有预防接种的 SVIR最优控制模型[J]. 西南大学学报(自然科学版),2015,37(1):72-78.
[4]何泽荣. 带年龄结构的种群动力系统的最优控制[D]. 西安:西安交通大学,2003.
[5]CAI L M,MODMAK C,WANG J. An age-structured model for cholera control with vaccination[J]. Applied mathematics and computation,2017,299:127-140.
[6]ANITA S. Analysis and control of age-dependent population dynamics[M]. Dordrecht,Boston,London:Kluwer Academic Publishers,2000.
[7]IANNELLI M. Mathematical theory of age-structured population dynamics[M]. Pisa:Giardini Editori E Stampatori,1995.
[8]BARBU V,IANNELLI M. Optimal control of population dynamics[J]. Journal of optimization theory and applications,1999,102(1):1-14.

相似文献/References:

[1]宋伊琳,崔景安.具有年龄结构的SIS模型的研究[J].南京师范大学学报(自然科学版),2006,29(02):21.
　Song Yilin,Cui Jingan.Study on SIS Model with Age Structure[J].Journal of Nanjing Normal University(Natural Science Edition),2006,29(01):21.
[2]郭中凯,王文婷,李自珍.具有脉冲免疫接种的SEIRS传染病模型分析[J].南京师范大学学报(自然科学版),2013,36(02):20.
　Guo Zhongkai,Wang Wenting,Li Zizhen.Dynamical Analysis of SEIRS Epidemic Model with Pulse Vaccination[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(01):20.

备注/Memo

备注/Memo:
收稿日期:2018-01-03.
基金项目:甘肃省高等学校科研项目(2015B-219).
通讯联系人:郭中凯,讲师,研究方向:控制理论与控制工程. E-mail:guozhongkai2010@outlook.com
更新日期/Last Update: 2019-03-30