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.
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.
作者
郭中凯
任秋艳
李建生
Guo Zhongkai;Ren Qiuyan;Li Jiansheng(College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 730050,China;College of Technology and Engineering,Lanzhou University of Technology,Lanzhou 730050,China)
出处
《南京师大学报（自然科学版）》
CAS
CSCD
北大核心
2019年第1期28-35,共8页
Journal of Nanjing Normal University(Natural Science Edition)
基金
甘肃省高等学校科研项目(2015B-219)
