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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(
)
《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]
- 卷:
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第42卷
- 期数:
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2019年01期
- 页码:
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28
- 栏目:
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·数学·
- 出版日期:
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2019-03-20
文章信息/Info
- Title:
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Optimal Control of Age-Structured SIR Epidemic Modelwith Vaccination and Treatment
- 文章编号:
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1001-4616(2019)01-0028-08
- 作者:
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郭中凯1; 2; 任秋艳1; 2; 李建生2
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(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):
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Guo Zhongkai1; 2; Ren Qiuyan1; 2; Li Jiansheng2
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(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)
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- 关键词:
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- Keywords:
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- 分类号:
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O157.13; Q141
- DOI:
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10.3969/j.issn.1001-4616.2019.01.006
- 文献标志码:
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A
- 摘要:
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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:
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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.
更新日期/Last Update:
2019-03-30