Effects of Age Structure, Contact Patterns and Vaccination on Transmission of the Hand-Foot-Mouth Disease

ZHOU Feng; ZHU Guanghu; TANG Tian

doi:10.21656/1000-0887.400175

Volume 41 Issue 5

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ZHOU Feng, ZHU Guanghu, TANG Tian. Effects of Age Structure, Contact Patterns and Vaccination on Transmission of the Hand-Foot-Mouth Disease[J]. Applied Mathematics and Mechanics, 2020, 41(5): 557-567. doi: 10.21656/1000-0887.400175

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Effects of Age Structure, Contact Patterns and Vaccination on Transmission of the Hand-Foot-Mouth Disease

doi: 10.21656/1000-0887.400175

¹School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, P.R.China;²Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, Guangxi 541004, P.R.China;³National Demonstration Center for Experimental Electronic Circuit Education, Guilin University of Electronic Technology, Guilin, Guangxi 541004, P.R.China

Funds: The National Natural Science Foundation of China（11661026）

Received Date: 2019-05-27
Rev Recd Date: 2019-09-23
Publish Date: 2020-05-01

Abstract

Abstract

In order to further reveal the transmission mechanism and optimize the immune strategy of the hand-foot-mouth disease (HFMD), a new HFMD transmission model was proposed under the effects of age structure, contact patterns and vaccination. The next generation matrix was used to calculate the basic reproduction number, and the theory of stability and dynamics was used to prove the existence and global stability of the disease-free and endemic equilibria. Finally numerical simulation was conducted to explore the effects of model parameters. It is found that age structure, contact matrices and vaccination have significant influence on the transmission, and the heterogeneity of age structure may worsen the infection, but quarantining patients and improving vaccination coverage vaccination rates can effectively help to control the disease. The results provide a scientific reference for the prevention and control of HFMD transmission.
- hand-foot-mouth disease,
- dynamic model,
- basic reproduction number,
- stability

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References(15)

References

[1]	KERMACK W O, MCKENDRICK A G. Contributions to the mathematical theory of epidemics[J]. Bulletin of Mathematical Biology,1991,53(1/2): 33-55.
[2]	马知恩, 周仓义, 王稳地, 等. 传染病动力学的数学建模与研究[M]. 北京: 科学出版社, 2004: 58-59.(MA Zhien, ZHOU Cangyi, WANG Wendi, et al. Mathematical Modeling and Research of Infectious Disease Dynamics [M]. Beijing: Science Press, 2004: 58-59.(in Chinese))
[3]	范琳烜, 唐三一. 寨卡病毒传播潜力与控制策略有效性分析[J]. 应用数学和力学, 2017,38(11): 1269-1278.(FAN Linxuan, TANG Sanyi. Analysis on transmission potential and control strategies of Zika virus[J]. Applied Mathematics and Mechanics,2017,38(11): 1269-1278.(in Chinese))
[4]	MI X L. Global dynamics of an SEIR epidemic model with vertical transmission[J]. SIAM Journal of Shanxi Normal University (Natural Science Edition),2013,62(1): 58-69.
[5]	MOGHADAS S M, GUMEL A B. An epidemic model for the transmission dynamics of HIV and another pathogen[J]. The ANZIAM Journal,2003,45(2): 181-193.
[6]	SCHMIDT N J, LENNETTE E H, HO H H. An apparently new enterovirus isolated from patients with disease of the central nervous system[J]. Journal of Infectious Diseases,1974,129(3): 304-309.
[7]	MA E, LAM T, CHAN K C, et al. Changing epidemiology of hand, foot, and mouth disease in Hong Kong, 2001—2009[J]. Japanese Journal of Infectious Diseases,2010,63(6): 422-426.
[8]	LAI C C, JIANG D S, WU H M, et al. A dynamic model for the outbreaks of hand, foot, and mouth disease in Taiwan[J]. Epidemiology and Infection,2016,144(7): 1500-1511.
[9]	ANG L W, KOH B K, CHAN K P, et al. Epidemiology and control of hand, foot and mouth disease in singapore[J]. Annals of the Academy of Medicine Singapore,2009,38(2): 106-112.
[10]	孙立梅, 邓爱萍, 康敏, 等. 2009—2010年广东省手足口病流行特征分析[J]. 华南预防医学, 2011,37(4): 9-13.(SUN Limei, DENG Aiping, KANG Min, et al. Epidemiological characteristics of hand-foot-mouth disease in Guangdong, 2009—2010[J]. South China Journal of Preventive Medicine,2011,〖STHZ〗 37(4): 9-13.(in Chinese))
[11]	胡跃华, 肖革新, 郭莹, 等. 2008—2011年中国大陆手足口病流行特征分析[J]. 中华疾病控制杂志, 2014,18(8): 693-697, 747.(HU Yuehua, XIAO Gexin, GUO Ying, et al. The epidemic features of the hand, foot, and mouth disease during 2008—2011 in China[J]. Chinese Journal of Disease Control,2014,18(8): 693-697, 747.(in Chinese))
[12]	仲连发, 张志诚, 赵继军. 基于年龄结构的中国大陆手足口病流行特性的分析[J]. 中华疾病控制杂志, 2015,19(7): 651-654, 687.(ZHONG Lianfa, ZHANG Zhicheng, ZHAO Jijun. Age-structured model and analysis of hand foot and mouth disease in China[J]. Chinese Journal of Disease Control,2015,19(7): 651-654, 687.(in Chinese))
[13]	VAN DEN DRIESSCHE P, WATMOUGH J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J]. Mathematical Biosciences,2002,180(1/2): 29-48.
[14]	ZHAO X, JING Z. Global asymptotic behavior in some cooperative systems of functional differential equations[J]. Canadian Applied Mathematics Quarterly,1996,4(4): 421-444.
[15]	贾斯月, 李靖欣, 朱凤才. 基于EV71疫苗接种的江苏省手足口病动力学模型研究[J]. 中华疾病控制杂志, 2019,23(3): 253-258.(JIA Siyue, LI Jingxin, ZHU Fengcai. A dynamic model of hand foot and mouth disease in Jiangsu Province based on EV71 vaccination[J]. Chinese Journal of Disease Control,2019,23(3): 253-258.(in Chinese)