| Study of the Optimal Integrated Control of a Dengue Transmission Model北大核心CSCD |
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| 引用本文： | 李雅芝,刘利利.Study of the Optimal Integrated Control of a Dengue Transmission Model北大核心CSCD[J].应用数学和力学,2022,43(4):445-452. |
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| 作者姓名： | 李雅芝 刘利利 |
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| 作者单位： | 1.黔南民族师范学院 数学与统计学院，贵州 都匀 558000 |
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| 基金项目： | 国家自然科学基金(11901326;11601293)；;贵州省科学技术基金(黔科合基础-ZK[2021]一般002)； |
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| 摘 要： | 建立了一个登革热在蚊子和人之间传播的模型，引入了Wolbachia、自我保护和杀虫剂三种控制措施，分别从常数控制和时变控制两个方面进行探讨。首先，分析了常数控制对模型基本再生数的影响，研究发现:Wolbachia有助于减小基本再生数，且基本再生数与自我保护和杀虫剂呈负相关。其次，以使得感染数最少且实施成本最低为目标，使用Pontryagin极值原理讨论最优控制。最后，通过数值模拟展示了最优控制的效果。
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| 关 键 词： | 登革热 传播模型 最优控制 数值模拟 |
| 收稿时间： | 2021-08-30 |
Study of the Optimal Integrated Control of a Dengue Transmission Model |
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| Li Y.,Liu L..Study of the Optimal Integrated Control of a Dengue Transmission Model[J].Applied Mathematics and Mechanics,2022,43(4):445-452. |
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| Authors: | Li Y Liu L |
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| Affiliation: | 1.School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun, Guizhou 558000, P.R.China2.Key Laboratory of Complex Systems and Intelligent Optimization of Qiannan,Duyun, Guizhou 558000, P.R.China3.Complex Systems Research Center, Shanxi University, Taiyuan 030006, P.R.China |
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| Abstract: | A transmission model for dengue fever between mosquitoes and human beings was established. Three control measures: Wolbachia, self-protection and insecticide were introduced. The constant control and the time-varying control were discussed respectively. Firstly, the influences of the constant control on the basic regeneration number of the model were analyzed. It is shown that Wolbachia helps reduce the basic regeneration number, and the basic regeneration number is negatively correlated with self-protection and insecticide. Secondly, in order to minimize the number of infections and the implementation cost, the optimal control was discussed with Pontryagin’s extreme value principle. Finally, the effects of the optimal control was demonstrated through numerical simulation. |
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| Keywords: | Dengue Numerical simulation Optimal control Transmission model |
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