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具有潜伏期时滞的时变SEIR模型的最优疫苗接种策略

王昕炜 彭海军 钟万勰

王昕炜, 彭海军, 钟万勰. 具有潜伏期时滞的时变SEIR模型的最优疫苗接种策略[J]. 应用数学和力学, 2019, 40(7): 701-712. doi: 10.21656/1000-0887.400048
引用本文: 王昕炜, 彭海军, 钟万勰. 具有潜伏期时滞的时变SEIR模型的最优疫苗接种策略[J]. 应用数学和力学, 2019, 40(7): 701-712. doi: 10.21656/1000-0887.400048
WANG Xinwei, PENG Haijun, ZHONG Wanxie. Optimal Vaccination Strategies for a Time-Varying SEIR Epidemic Model With Latent Delay[J]. Applied Mathematics and Mechanics, 2019, 40(7): 701-712. doi: 10.21656/1000-0887.400048
Citation: WANG Xinwei, PENG Haijun, ZHONG Wanxie. Optimal Vaccination Strategies for a Time-Varying SEIR Epidemic Model With Latent Delay[J]. Applied Mathematics and Mechanics, 2019, 40(7): 701-712. doi: 10.21656/1000-0887.400048

具有潜伏期时滞的时变SEIR模型的最优疫苗接种策略

doi: 10.21656/1000-0887.400048
详细信息
    作者简介:

    王昕炜(1992—),男,博士生(E-mail: wangxinwei@mail.dlut.edu.cn);彭海军(1982—),男,副教授(通讯作者. E-mail: hjpeng@dlut.edu.cn);钟万勰(1934—),男,教授,中科院院士(E-mail: zwoffice@dlut.edu.cn).

  • 中图分类号: O232

Optimal Vaccination Strategies for a Time-Varying SEIR Epidemic Model With Latent Delay

  • 摘要: 该文在经典SEIR仓室模型的基础上,在由潜伏个体转化为感染个体的过程中,引入了时滞参数以刻画潜伏期的特性.同时,将传染系数改写为季节性变化参数,并通过引入疫苗接种和时变的成功免疫率,形成了含有时滞受控的时变SEIR模型.进一步地,在状态时滞最优控制问题的框架下,以疫苗接种率为控制变量,求解了基于该模型的传染病最优疫苗接种策略.在最优控制问题中,同时考虑了控制约束、易感染人口数上限、时变的疫苗产量上限三类约束.使用多区段的保辛伪谱方法对该问题进行求解.数值结果表明,计算得到的控制策略可以有效抑制传染病的传播.不同算例之间的对比说明忽略时变因素可能导致不合理的接种策略.
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出版历程
  • 收稿日期:  2019-01-28
  • 修回日期:  2019-05-10
  • 刊出日期:  2019-07-01

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