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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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.
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.
引文
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[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.