儿童手足口病的数学建模和计算机模拟

Abstract

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

CLC Number:

O175.12

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.

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Figures/Tables 8

References 30

1	Huang Y , Deng T , Yu S C , et al. Effect of meteorological variables on the incidence of hand, foot, and mouth disease in children:a time-series analysis in Guangzhou, China. BMC Infectious Diseases, 2013, 13: 134 doi: 10.1186/1471-2334-13-134
2	中国疾病控制中心.手足口病疾病概述.http://www.chinacdc.cn/jkzt/crb/bl/szkb/zstd/201212/t2012121072846.html
	Chinese center for disease control and prevention. The overview for Hand-Foot-Mouth Disease. http://www.chinacdc.cn/jkzt/crb/bl/szkb/zstd/201212/t2012121072846.html
3	李超贤, 赵伟. 中西医结合治疗手足口病100例. 上海中医药杂志, 2009, 43 (9): 35- 36
	Li C X , Zhao W . Treatment of 100 cases of Hand-Foot-Mouth Disease by integrative Chinese and Western Medicine. Shanghai Journal of Traditional Chinese Medicine, 2009, 43 (9): 35- 36
4	Seddon J H , Duff M F . Hand-foot-and-mouth disease:coxsackievirus types A5, A10, and A16 infections. N Z Med J, 1971, 74: 368- 373
5	Robinson C R , Doane F W , Rhodes A J . Report of an outbreak of febrile illness with pharyngeal lesions and exanthem:Toronto, summer 1957-isolation of group a coxsackie virus. The Canadian Medical Association Journal, 1958, 79 (8): 615- 621
6	Schmidt N J , Lennette E H , Ho H H . An apparently new enterovirus isolated from patients with disease of the central nervous system. The Journal of Infectious Diseases, 1974, 129 (3): 304- 309 doi: 10.1093/infdis/129.3.304
7	Repass L G , Palmer W C , Stancampiano F F . Hand, foot, and mouth disease:identifying and managing an acute viral syndrome. Clevel Clin J Med, 2014, 81: 537- 543 doi: 10.3949/ccjm.81a.13132
8	公共卫生数据中心.手足口病.http://www.phsciencedata.cn/Share/kysjml.jsp?id=b9c93769-3e0f-413a-93c1-027d2009d8bc&show=0
	Public health data center. Hand, foot, and mouth disease.http://www.phsciencedata.cn/Share/kysjml.jsp?id=b9c93769-3e0f-413a-93c1-027d2009d8bc&show=0
9	洪志恒, 常昭瑞, 涂文校, 等. 2016年3月全国突发公共卫生事件及需关注的传染病风险评估. 疾病监测, 2016, 31 (03): 181- 184
	Hong Z H , Chang Z R , Tu R Q , et al. Risk assessment of public health emergencies and communicable diseases concerned in the mainland of China, March 2016. Disease Surrveillance, 2016, 31 (3): 181- 184
10	Wang J R , Tuan Y C , Tsai H P . Change of major genotype of enterovirus71 in outbreaks of hand-footand-mouth disease in tai wan between 1998 and 2000. J Clin Micro Biol, 2002, 40: 10- 15 doi: 10.1128/JCM.40.1.10-15.2002
11	Fujimoto T , Chikahira M , Yoshida S , et al. Outbreak of central nervous system disease associated with hand, foot, and mouth disease in Japan during the summer of 2000:detection and molecular epidemiology of enterovirus 71. Microbiol Immunol, 2002, 46: 621- 627 doi: 10.1111/mim.2002.46.issue-9
12	Chua K B , Kasri A R . Hand foot and mouth disease due to enterovirus 71 in malaysia. Virol Sin, 2011, 26: 221- 228 doi: 10.1007/s12250-011-3195-8
13	Zhang Y , Tan X , Wang H , et al. An outbreak of hand, foot, and mouth disease associated with subgenotype C4 of human enterovirus 71 in Shandong. China J Clin Virol, 2009, 44: 262- 267 doi: 10.1016/j.jcv.2009.02.002
14	国家卫生计生委疾病预防控制局.卫生部关于将手足口病纳入法定传染病管理的通知.http://www.moh.gov.cn/jkj/s3577/200805/1a8bb3668b7d4540afb0531dfcef978d.shtml
	Bureau of disease control and prevention of national health council of the People's Republic of China. The notice of the Ministry of health on hand foot and mouth disease into legal communicable diseases management. http://www.moh.gov.cn/jkj/s3577/200805/1a8bb3668b7d4540afb0531dfcef978d.shtml
15	Wang L , Zhu B , Li Z , et al. Epidemiologic characteristics of hand, foot, and mouth disease in China from 2006 to 2015. J Infect, 2016, 73: 512- 515 doi: 10.1016/j.jinf.2016.08.007
16	Tiing F C S , Labadin J . A Simple Deterministic Model for the Spread of Hand, Foot and Mouth Disease (hfmd) in Sarawak//Second Asia International Conference on Modeling and Simulation. Kuala Lumpur, Malaysia:IEEE, 2008, 947- 952
17	Liu J L . Threshold dynamics for a HFMD epidemic model with periodic transmission rate. Nonlinear Dynamics, 2011, 64: 89- 95 doi: 10.1007/s11071-010-9848-6
18	MaY J , Liu M X , Hou Q , et al. Modeling seasonal HFMD with the recessive infection in shandong. China Math Biosci Eng, 2013, 10: 1159- 1171 doi: 10.3934/mbe
19	Yang J Y , Chen Y M , Zhang F Q . Stability analysis and optimal control of a hand-foot-mouth disease (hfmd) model. J Appl Math Comput, 2013, 41: 99- 117 doi: 10.1007/s12190-012-0597-1
20	Li Y , Zhang J H , Zhang X A . Modeling and preventive measures of hand, foot and mouth disease(hfmd) in china. International Journal of Environmental Research and Public Health, 2014, 11 (3): 3108- 3117 doi: 10.3390/ijerph110303108
21	Li Y , Wang L W , Pang L Y , et al. The data fitting and optimal control of a hand, foot and mouth disease (HFMD) model with stage structure. Applied Mathematics and Computation, 2016, 276: 61- 74 doi: 10.1016/j.amc.2015.11.090
22	Wang J Y , Xiao Y N , Peng Z H . Modeling seasonal HFMD infections with the effects of contaminated environments in mainland China. Applied Mathematics and Computation, 2016, 274: 615- 627 doi: 10.1016/j.amc.2015.11.035
23	Wang J Y , Xiao Y N , Cheke R A . Modeling the effects of contaminated environments on HFMD infections in mainland China. Biosystems, 2016, 140: 1- 7 doi: 10.1016/j.biosystems.2015.12.001
24	Chou A H , Liu C C , Chang P C , et al. Pilot scale production of highly efficacious and stable enterovirus 71 vaccine candidates. PloS One, 2012, 7: e34834 doi: 10.1371/journal.pone.0034834
25	Liang Z , Mao Q , Gao F , et al. Progress on the research and development of human enterovirus 71(ev71) vaccines. Front Med, 2013, 7: 111- 121 doi: 10.1007/s11684-012-0237-z
26	Zhu F C , Xu W B , Xia J L , et al. Efficacy, safety, and immunogenicity of an enterovirus 71 vaccine in China. N Engl J Med, 2014, 370 (9): 818- 828 doi: 10.1056/NEJMoa1304923
27	中华人民共和国国家卫生委科技教育司.重大新药创制科技重大专项取得重大成果——世界首个预防手足口病疫苗获批生产上市.http://www.nhfpc.gov.cn/qjjys/s3594r/201512/fa403581683d4b619bcee477aa15423e.shtml
	Department of science and technology education of national health council of the People's Republic of China. Creative technology of major new drugs made significant achievements and hand foot and mouth disease prevention vaccine in the world was firstly approved to be manufactured and marketed.http://www.nhfpc.gov.cn/qjjys/s3594r/201512/fa403581683d4b619bcee477aa15423e.shtml
28	Zhang X A , Zhao Y D , Neumann A U . Partial immunity and vaccination for influenza. J Comput Biol, 2010, 17 (12): 1689- 1696 doi: 10.1089/cmb.2009.0003
29	Van den Driessche P , Watmough J . Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 2002, 180 (1): 29- 48
30	Li R C , Liu L D , Mo Z J , et al. An inactivated enterovirus 71 vaccine in healthy children. N Engl J Med, 2014, 370 (9): 829- 837 doi: 10.1056/NEJMoa1303224

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

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