Threshold dynamics for a HFMD epidemic model with periodic transmission rate. (English) Zbl 1280.92062

Summary: In this paper, a periodic epidemic model is proposed in order to simulate the dynamics of HFMD transmission. We consider the effects of quarantine in the children population. We obtain a threshold value which determines the extinction and uniform persistence of the disease. Our results show that the disease-free equilibrium is globally asymptotically stable if the threshold value is less than unity. Otherwise, the system has a positive periodic solution and the disease persists. Numerical simulations show that quarantine has a positive impact on the spread of disease, i.e., quarantine is beneficial to the intervention and control of the disease outbreak in the children population.


92D30 Epidemiology
34C25 Periodic solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
Full Text: DOI


[1] Reports from Sarawak Health Department. http://www.sarawak.health.gov.my/hfmd.htm#INFO9
[2] Centers for Disease Control and Prevention (CDC): Deaths among children during an outbreak of hand, foot, and mouth disease–Taiwan, Republic of China, April–July 1998. MMWR Morb. Mortal. Wkly. Rep. 47, 629–632 (1998). PMID 9704628. http://www.cdc.gov/mmwr/preview/mmwrhtml/00054640.htm
[3] Ho, M., Chen, E.R., Hsu, K.H., Twu, S.J., Chen, K.T., Tsai, S.F., Wang, J.R., Shih, S.R.: An epidemic of enterovirus 71 infection in Taiwan. Taiwan Enterovirus Epidemic Working Group. N. Engl. J. Med. 341, 929–935 (1999) · doi:10.1056/NEJM199909233411301
[4] The Hindu: Kerala News: Outbreak of rare child disease in Malappuram. http://www.hindu.com/2005/11/17/stories/2005111706880700.htm
[5] Viral epidemic maintains grip in China, with three more deaths. http://news.xinhuanet.com/english/2008-05/14/content_8167664.htm . Accessed 15 May 2008
[6] Mass intestinal virus infection kills 19 children–XinHuaNet.com. http://news.xinhuanet.com/english/2008-04/27/content_8061094.htm . Retrieved on 2 May 2008
[7] Mass intestinal virus infection in east China up to 2477, kills 21–XinHuaNet.com. http://news.xinhuanet.com/english/2008-05/01/content_8088299.htm . Retrieved on 2 May 2008
[8] China on alert as virus spreads. http://news.bbc.co.uk/1/hi/world/asia-pacific/7381741.stm
[9] Spreading virus kills 28 children. http://www.cnn.com/2008/WORLD/asiapcf/05/07/china.virus/index.html . Retrieved on 7 May 2008
[10] BBC NEWS/World/Asia-Pacific: China virus toll continues rise. http://news.bbc.co.uk/2/hi/asia-pacific/7383796.stm
[11] China on alert over deadly child virus. http://edition.cnn.com/2008/WORLD/asiapcf/05/03/china.virus/index.html?eref=rss_topstories . Retrieved on 3 May 2008
[12] Suhaimi, Nur Dianah: HFMD: 1000 cases a week is unusual, says doc, Singapore: The Sunday Times (Straits Times). 1–2, 20 April 2008
[13] Viet Nam News: HFMD cases prompt tighter health screening at airport. http://vietnamnews.vnagency.com.vn/showarticle.php?num=01HEA150508 . Accessed 15 May 2008
[14] EV-71 virus continues dramatic rise. http://ubpost.mongolnews.mn/index.php?option=com_content&task=view&id=1847&Itemid=1 . Accessed 23 May 2008
[15] http://www.bt.com.bn/en/home_news/2008/11/07/1_053_hfmd_cases_recorded
[16] Tiing, F.C.S., Labadin, J.: A simple deterministic model for the spread of hand, foot and mouth disease (HFMD) in Sarawak. In: 2008 Second Asia International Conference on Modelling & Simulation, pp. 947–952 (2008)
[17] Wang, Y.C., Sung, F.C.: Modeling the infectious for Enteroviruses in Taiwan. http://gra103.aca.ntu.edu.tw/gdoc/D91844001a.pdf,2004 . Retrieved 21 July 2007
[18] Urashima, M., Shindo, N., Okabe, N.: Seasonal models of herpangina and hand-foot-mouth disease to simulate annual fluctuations in urban warming in Tokyo. Jpn. J. Infect. Dis. 48–53 (2003)
[19] Zhang, F., Zhao, X.-Q.: A periodic epidemic model in a patchy environment. J. Math. Anal. Appl. 325(1), 496–516 (2007) · Zbl 1101.92046 · doi:10.1016/j.jmaa.2006.01.085
[20] Nakata, Y., Kuniya, T.: Global dynamics of a class of SEIRS epidemic models in a periodic environment. J. Math. Anal. Appl. 363, 230–237 (2010) · Zbl 1184.34056 · doi:10.1016/j.jmaa.2009.08.027
[21] Wang, W., Zhao, X.-Q.: Threshold dynamics for compartmental epidemic models in periodic environments. J. Dyn. Differ. Equ. 20(3), 699–717 (2008) · Zbl 1157.34041 · doi:10.1007/s10884-008-9111-8
[22] Zhao, X.-Q.: Dynamical Systems in Population Biology. Springer, New York (2003) · Zbl 1023.37047
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