年龄结构流感模型综合控制策略研究

数学物理学报 ›› 2024, Vol. 44 ›› Issue (3): 804-814.

• • 上一篇

年龄结构流感模型综合控制策略研究

杨俊元^*(),张晨琳,杨丽

山西大学复杂系统研究所太原030006;山西省疾病防控的数学技术与大数据分析重点实验室太原 030006

收稿日期:2023-05-15 修回日期:2023-10-07 出版日期:2024-06-26 发布日期:2024-05-17
通讯作者: *杨俊元，E-mail:yjyang66@sxu.edu.cn
基金资助:
教育部人文社科一般项目(22YJAZH129);国家自然科学基金(12001339);国家自然科学基金(61573016);国家自然科学基金(12271143);山西省回国留学人员科研教研资助项目(2023-024);山西省自然科学基金(20210302123454)

Study on Comprehensive Control Strategies of an Age Structured Influenza Model

Yang Junyuan^*(),Zhang Chenlin,Yang Li

Complex System Research Center, Shanxi University, Taiyuan 030006;Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006

Received:2023-05-15 Revised:2023-10-07 Online:2024-06-26 Published:2024-05-17
Supported by:
Humanities and Social Foundation of Ministry of Education of China(22YJAZH129);National Natural Science Foundation of China(12001339);National Natural Science Foundation of China(61573016);National Natural Science Foundation of China(12271143);Shanxi Scholarship Council of China(2023-024);Shanxi Province Science Foundation(20210302123454)

摘要/Abstract

摘要：

该文考虑流感的年龄异质性, 结合流感传播机理建立了连续年龄结构的 SIR 流感模型. 引入了疫苗接种和实施治疗两种控制措施, 提出成本效益函数, 利用庞特利亚金最大值原理及 Ekland 变分原理得到最优控制的存在性. 通过向前和向后扫描算法进行数值模拟. 比较多种控制策略, 发现接种疫苗和实施治疗组合控制效果最佳; 比较成本效应, 发现低成本的控制效果最理想. 最后综合分析得出接种疫苗成本效益最高, 而同时实施接种和治疗公共卫生效率最佳.

关键词: 流感, 庞特里亚金最大值原理, 最优控制, Ekland 变分原理

Abstract:

In this paper, we combine the age heterogeneity and the mechanisms of influenza to build an age structured SIR influenza model. Then we introduce two control variables-vaccination and treatment and propose the benefitial functional. Using the Pontryagin maximum principle and Ekland variant principle, we obtain the existence and uniqueness of the optimal control problem. Moreover, we employ forward and backward algorithms to do numerical experiments. Compared the results of many control measures, it is concluded that the combination of vaccination and treatment has the best control effect and furthermore, low-cost strategy is the best. Finally, through comprehensive analysis, vaccination has a best benefit from cost points of view and a combined measure has a best effect from public health perspectives.

Key words: Influenza model, Pontryagin maximum principle, Optimal control, Ekland variant principle

中图分类号:

O232

杨俊元, 张晨琳, 杨丽. 年龄结构流感模型综合控制策略研究[J]. 数学物理学报, 2024, 44(3): 804-814.

Yang Junyuan, Zhang Chenlin, Yang Li. Study on Comprehensive Control Strategies of an Age Structured Influenza Model[J]. Acta mathematica scientia,Series A, 2024, 44(3): 804-814.

图/表 6

图1

图2

表1

图3

表2

图4

参考文献 16

[1]	Li X Z, Yang J Y, Martcheva M. Age Structured Epidemic Modeling. Switzerland: Springer Nature, 2020
[2]	凌云, 狄亚敏, 陆青青, 李烁. 流行性感冒的病原学特征及其药物治疗进展. 解放军药学学报, 2018, 34(02): 159-164
	Ling Y, Di Y M, Lu Q Q, Li S. Pathogenic characteristics of influenza and its drug treatment progress. Pharm J Chin PLA, 2018, 34(2): 159-164
[3]	罗道清. 接种流感疫苗对流感疾病的预防控制作用分析. 临床医学工程, 2020, 27(08): 1035-1036
	Luo D Q. Analysis of prevention and control effect of influneza vaccination on influenza diseases. Clinical Medicine & Engineering, 2020, 27(08): 1035-1036
[4]	Matrajt L, Longini Jr I M. Optimizing vaccine allocation at different points in time during an epidemic. PLoS One, 2010, 5(11): e13767
[5]	Nuno M, Castillo-Chavez C, Feng Z, Martcheva M. Mathematical models of influenza: The role of cross-immunity, quarantine and age-structure//Brauer F, van den Driessche P, Wu J, eds. Mathematical Epidemiology. Lecture Notes in Mathematics, vol 1945. Heidelberg: Springer, 2008: 349-364
[6]	Patel R, Longini I M Jr, Halloran M E. Finding optimal vaccination strategies for pandemic influenza using genetic algorithms. Journal of Theoretical Biology, 2005, 234: 201-212 pmid: 15757679
[7]	邱守中, 潘利花, 梁夏楠, 等. 流感疫苗接种对儿童流感预防的有效性与安全性分析. 医学动物防制, 2022, 38(05): 505-506
	Qiu S Z, Pan L H, Liang X N, et al. Analysis on efficacy and safety of inluenza vaccination against influence in children. Journal of Medical Pest Control, 2022, 38(05): 505-506
[8]	Read J M, Lessler J, Riley S, et al. Social mixing patterns in rural and urban areas of southern China. Proceedings of the Royal Society B: Biological Sciences, 2014, 281(1785): 20140268
[9]	随海田, 郭洋, 赵杰, 等. 流感疫苗在高危人群中应用安全性、有效性及接种现状研究新进展. 中华流行病学杂志, 2022, 43(3): 436-439 doi: 10.3760/cma.j.cn112338-20210227-00153 pmid: 35345303
	Sui H T, Guo Y, Zhao J, et al. New progress in research on the safety, effectiveness, and vaccination status of influenza vaccines in high-risk populations. Chinese Journal of Epidemiology, 2022, 43(3): 436-439 doi: 10.3760/cma.j.cn112338-20210227-00153 pmid: 35345303
[10]	向蓥飞, 周德谦, 钟杰伟, 等. 广州市越秀区托幼机构流感样病例暴发疫情经济负担评估和流感疫苗卫生经济学评价. 华南预防医学, 2021, 47(10): 1231-1235
	Xiang Y F, Zhou D Q, Zhong W J, et al. Evaluation of the economic burden of influenza like cases outbreak and health economics of influenza vaccines in nursery and child care institutions in Yuexiu district, Guangzhou city. South China Journal of Preventive Medicine, 2021, 47(10): 1231-1235
[11]	张春国. 流行性感冒的药物治疗分析. 世界最新医学信息文摘, 2015, 15(18): 78
	Zhang C G. Analysis of drug therapy for influenza. World Latest Medicne Information, 2015, 15(18): 78
[12]	赵宏婷, 范思萌, 杨孝坤, 等. 季节性流感在不同年龄人群中的临床特征及严重程度研究概述. 国际病毒学杂志, 2021, 28(05): 424-427
	Zhao H T, Fan S M, Yang X K, et al. Review of clinical characteristics and severity of seasonal influenza in different age groups. International Journal of Virology, 2021, 28(05): 424-427
[13]	赵双雨, 董书衡, 李欣辰, 等. 中国流感疫苗优先推荐接种人群疫苗犹豫现状及影响因素. 中国预防医学杂志, 2021, 22(10): 798-803
	Zhao S Y, Dong S H, Li X C, et al. The current situation and influencing factors of hesitancy in recommending influenza vaccines to priority recipients in China. Chin Prev Med, 2021, 22(10): 789-803
[14]	中国公共卫生科学数据中心. https://www.phsciencedata.cn/Share/kysjml.jsp?id=c6f2fbd7-a11a-426f-b9fb-fa3ce0c1b8b4
[15]	Zhou L, Su Q, Xu I, et al. Seasonal influenza vacation coverage rate of target groups in selected cities and provinces in China by season(20009/10 to 2011/12). PLoS One, 2013, 8(9): e73724
[16]	http://www.stats.gov.cn/tjsj/pcsj/rkpc/6rp/indexch.htm. [2023-04-01]

年龄结构流感模型综合控制策略研究

Study on Comprehensive Control Strategies of an Age Structured Influenza Model

RichHTML

PDF (PC)

摘要/Abstract

引用本文

使用本文

图/表 6

参考文献 16

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	宾茂君, 施翠云. 半线性Riemann-Liouville分数阶发展方程反馈时间最优控制[J]. 数学物理学报, 2024, 44(3): 687-698.
[2]	钟毅, 王毅, 蒋添合. 一类具有无症状感染和隔离的 SIAQR 传播模型动力学分析和最优控制[J]. 数学物理学报, 2023, 43(6): 1914-1928.
[3]	卢维平,刘汉兵. 全空间中带位势热方程的采样时间最优控制[J]. 数学物理学报, 2023, 43(4): 1269-1283.
[4]	曾彪. 一类带有弱连续算子的发展方程的最优控制[J]. 数学物理学报, 2023, 43(2): 515-530.
[5]	崔骁勇,张灿. 一类带指数权最优控制问题的Turnpike性质[J]. 数学物理学报, 2022, 42(4): 1256-1264.
[6]	何泽荣,窦艺萌,韩梦杰. 具有尺度等级和时滞的种群系统的最优边界控制[J]. 数学物理学报, 2022, 42(3): 867-880.
[7]	何泽荣,周楠. 具有年龄等级结构的种群竞争系统的最优收获控制[J]. 数学物理学报, 2022, 42(1): 228-244.
[8]	何泽荣,韩梦杰. 带时滞的尺度等级结构种群系统的最优初始控制[J]. 数学物理学报, 2021, 41(4): 1181-1191.
[9]	刘琼琳,唐应辉. 在$D$-策略控制下服务员单重休假且休假不中断的$M$/$G$/1排队系统分析[J]. 数学物理学报, 2021, 41(1): 269-288.
[10]	罗乐,唐应辉. 具有p-进入规则和Min(N, D, V)-策略的M/G/1排队系统容量问题研究[J]. 数学物理学报, 2019, 39(5): 1228-1246.
[11]	唐矛宁,孟庆欣. 带跳跃平均场倒向随机微分方程的线性二次最优控制[J]. 数学物理学报, 2019, 39(3): 620-637.
[12]	潘取玉,唐应辉. 在延迟Min (N, D)-策略M/G/1可修排队系统及最优控制策略[J]. 数学物理学报, 2018, 38(5): 1014-1031.
[13]	章春国, 刘宇标, 刘维维. Timoshenko梁的边界最优控制[J]. 数学物理学报, 2018, 38(3): 454-466.
[14]	高丽君, 唐应辉. 具有Min(N,D)-策略控制的M/G/1可修排队系统及最优控制策略[J]. 数学物理学报, 2017, 37(2): 352-365.
[15]	何泽荣, 杨立志. 具有尺度结构和双加权的种群模型:稳定性与最优收获[J]. 数学物理学报, 2016, 36(3): 584-600.