儿童手足口病的数学建模和计算机模拟

数学物理学报 ›› 2018, Vol. 38 ›› Issue (5): 1032-1040.

• 论文 • 上一篇

儿童手足口病的数学建模和计算机模拟

李华^1,⁴(),刘三红^2,*,方奕乐³,张兴安¹

¹ 华中师范大学数学与统计学学院武汉 430079
² 湖北科技学院数学与统计学院湖北咸宁 437100
³ 武昌首义学院机电与自动化学院武汉 430064
⁴ 西安市长安区第三中学西安 710000

收稿日期:2017-05-24 出版日期:2018-10-26 发布日期:2018-11-09
通讯作者: 刘三红 E-mail:lihua11230908@163.com
作者简介:李华, E-mail: lihua11230908@163.com
基金资助:
国家自然科学基金(11371161);国家自然科学基金(11071275);华中师范大学中央高校基本科研业务费(CCNU16JCZX10);湖北科技学院教学研究基金(2016-XA-008)

Mathematical Modeling and Computer Simulation on Hand, Foot and Mouth Disease in Children

Hua Li^1,⁴(),Sanhong Liu^2,*,Yile Fang³,Xingan Zhang¹

¹ School of Mathematics and Statistics, Central China Normal University, Wuhan 430079
² School of Mathematics and Statistics, Hubei University of Science and Technology, Hubei Xianning 437100
³ School of Electromechanical and Automation, WuChang ShouYi Unviversity, Wuhan 430064
⁴ Xi'an Changan District No.3 Middle School, Xi'an 710000

Received:2017-05-24 Online:2018-10-26 Published:2018-11-09
Contact: Sanhong Liu E-mail:lihua11230908@163.com
Supported by:
the NSRC(11371161);the NSRC(11071275);the Self-Determined Research Funds of CCNU from the Colleges' Basic Research and Operation of MOE(CCNU16JCZX10);the Teaching Research Fund from Hubei University of Science and Technology(2016-XA-008)

摘要/Abstract

摘要：

手足口病（HFMD）是由肠道病毒引起的传染病，患者主要是少儿，由EV71和CoxA16病毒引起.该文建立了传染病SEIHRS模型，模拟了2012-2016年手足口病患病者的数据，估计了手足口病每年的基本再生数，给出了手足口病少儿疫苗的接种率，预测了2017年手足口病患病者的数目并提出了预防控制策略.该文的结果能为该疾病的预防与控制工作提供理论依据.

关键词: 手足口病, 基本再生数, 数据模拟, EV71疫苗, 免疫接种率

Abstract:

Hand, foot, and mouth disease (HFMD) is a contagious disease mainly caused by the enterovirus 71 (EV71) and coxsackievirus A 16 (CoxA16). The infectious of HFMD is mainly children. In this paper, we construct an SEIHRS model, simulate the HFMD data of infectious from 2012 to 2016, estimate the basic reproductive number each year from 2012 to 2016, predict the infectious number of HFMD in year 2017, compute the domain of vaccination rate on children and put forward the preventive measures and control strategy. The results of this paper can provide a theory basis for disease control and prevention of HFMD.

Key words: Hand, foot, and mouth disease, Basic reproductive number, Data simulation, EV71 vaccination, Immunization coverage rate

中图分类号:

O175.12

李华,刘三红,方奕乐,张兴安. 儿童手足口病的数学建模和计算机模拟[J]. 数学物理学报, 2018, 38(5): 1032-1040.

Hua Li,Sanhong Liu,Yile Fang,Xingan Zhang. Mathematical Modeling and Computer Simulation on Hand, Foot and Mouth Disease in Children[J]. Acta mathematica scientia,Series A, 2018, 38(5): 1032-1040.

图/表 8

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图 3

参考文献 30

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月份/年份	2012	2013	2014	2015	2016
一月	47526	56956	51003	57763	79499
二月	41614	33261	40646	33003	32457
三月	100575	88724	162486	61378	72464
四月	248855	172499	430024	173384	226430
五月	454651	255533	523743	287235	442075
六月	374749	303423	474419	354308	452668
七月	113922	154213	140151	180813	171581
九月	138875	182317	197059	180074	134972
十月	142617	127566	207550	160106	177639
十一月	147403	105061	149732	130829	217754
十二月	122506	94435	99201	116239	145558

参数及其范围	来源	2012	2013	2014	2015	2016
β∈[0, 50]	MSS	1.078	1.0502	1.0791	0.9819	0.7256
γ₁∈[0, 1]	MSS	1.0000	0.9999	0.9997	0.9454	0.6643
γ₂∈[0, 1]	MSS	1.0000	1.0000	0.9998	0.9477	0.9944
α∈[0, 1]	MSS	1.0000	1.0000	0.9590	1.0000	0.9959
ρ∈[0, 1]	MSS	0.0591	0.1227	0.0879	0.1608	0.0384
γ₃∈[0, 1]	MSS	0.0106	0.0042	0.0087	0.0025	0.0109
E(0)	MSS	4000	4000	3000	3279	3800
I(0)	MSS	3300	2177	2994	3299	3799
H(0)	MSS	4000	4000	3000	3300	3796
R₀	Calculated	1.0778	1.0448	1.0792	1.0380	1.0919

年份	2012	2013	2014	2015	2016
卡方值(χ²)	0.1163	0.1033	0.1678	0.1393	0.3158
自由度	2	2	2	2	2
临界值	5.991	5.991	5.991	5.991	5.991
临界值是在自由度为2的χ²分布的0.05的上侧分位点

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儿童手足口病的数学建模和计算机模拟

Mathematical Modeling and Computer Simulation on Hand, Foot and Mouth Disease in Children

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