| 具有潜伏期时滞的时变SEIR模型的最优疫苗接种策略 |
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| 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. |
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| 作者姓名： | 王昕炜 彭海军 钟万勰 |
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| 作者单位： | 大连理工大学 工业装备结构分析国家重点实验室, 辽宁 大连 116023 |
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| 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,形成了含有时滞的时变受控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3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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| 关 键 词： | SEIR模型 时滞 最优控制 疫苗接种策略 保辛伪谱方法 |
| 收稿时间： | 2019-01-28 |
Optimal Vaccination Strategies for a Time-Varying SEIR Epidemic Model With Latent Delay |
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| 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. |
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| Authors: | WANG Xinwei PENG Haijun ZHONG Wanxie |
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| Affiliation: | State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China |
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| Abstract: | On the basis of the classic SEIR compartmental model, a time-delayed term was introduced to characterize the latent delay. Furthermore, a controlled time-varying SEIR model with delay was established in view of the vaccination, the successfully immune rate and the seasonally varying incidence coefficient. Meanwhile, the optimal vaccination strategy was determined under the frame of the optimal control problem with the vaccination rate taken as the control variable. In the formulated optimal control problem, 3 kinds of constraints (i.e., the constraints on control, the upper limit on the susceptible population and the time-varying upper limit on the vaccination supply) were considered. The optimal control problem was numerically solved with a multi-interval symplectic pseudospectral method. Numerical results demonstrate that the obtained vaccination strategy can effectively suppress the spread of the disease, and the comparison between different cases suggests that omitting time-varying factors may result in unreasonable vaccination strategies. |
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| Keywords: | SEIR model time delay optimal control vaccination strategy symplectic pseudospectral method |
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