Abstract and Applied Analysis

A Spatial-Temporal ARMA Model of the Incidence of Hand, Foot, and Mouth Disease in Wenzhou, China

Jie Li, Yanjun Fu, Ancha Xu, Zumu Zhou, and Weiming Wang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


To investigate the variability of HFMD in each county of Wenzhou, a spatial-temporal ARMA model is presented, and a general Bayesian framework is given for parameter estimation. The proposed model has two advantages: (i) allowing time series to be correlated, thus it can describe the series both spatially and temporally; (ii) implementing forecast easily. Based on the HFMD data in Wenzhou, we find that HFMD had positive spatial autocorrelation and the incidence seasonal peak was between May and July. In the county-level analysis, we find that after first-order difference the spatial-temporal ARMA ( 0 , 0 ) × ( 1 , 0 ) 12 model provides an adequate fit to the data.

Article information

Abstr. Appl. Anal., Volume 2014 (2014), Article ID 238724, 9 pages.

First available in Project Euclid: 2 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Li, Jie; Fu, Yanjun; Xu, Ancha; Zhou, Zumu; Wang, Weiming. A Spatial-Temporal ARMA Model of the Incidence of Hand, Foot, and Mouth Disease in Wenzhou, China. Abstr. Appl. Anal. 2014 (2014), Article ID 238724, 9 pages. doi:10.1155/2014/238724. https://projecteuclid.org/euclid.aaa/1412273214

Export citation


  • Centers for Disease Control and Prevention, “About hand, foot, and mouth disease,” http://www.cdc.gov/hand-foot-mouth/.
  • Chinese Center for Disease Control and Prevention, “The 2012 annual national notifiable communicable disease situation,” http://www.chinacdc.cn/.
  • M. Y. Liu, W. Liu, J. Luo et al., “Characterization of an outbreak of hand, foot, and mouth disease in nanchang, China in 2010,” PLoS ONE, vol. 6, no. 9, Article ID e25287, 2011.
  • M. Hu, Z. Li, J. Wang et al., “Determinants of the incidence of hand, foot and mouth disease in China using geographically weighted regression models,” PloS ONE, vol. 7, no. 6, Article ID e38978, 2012.
  • Y. Liu, X. Wang, Y. Liu et al., “Detecting spatial-temporal clusters of hfmd from 2007 to 2011 in Shandong province, China,” PloS ONE, vol. 8, no. 5, Article ID e63447, 2013.
  • N. Sarma, “Hand, foot, and mouth disease: current scenario and Indian perspective,” Indian Journal of Dermatology, Venereology, and Leprology, vol. 79, no. 2, pp. 165–175, 2013.
  • Zhejiang online source for disease control and prevention, “The statistic results of “ten legal infectious diseases” in Zhejiang province in 2012,” (Chinese), http://www.cdc.zj.cn/.
  • F. Chuo, S. Tiing, and J. Labadin, “A simple deterministic model for the spread of hand, foot and mouth disease (HFMD) in Sarawak,” in Proceedings of the 2nd Asia International Conference on Modelling and Simulation (AMS '08), pp. 947–952, IEEE, May 2008.
  • N. Roy and N. Haider, “Compartmental modeling of hand, foot and mouth infectious disease (HFMD),” Research Journal of Applied Sciences, vol. 5, no. 3, pp. 177–182, 2010.
  • N. Roy, “Mathematical modeling of hand-foot-mouth disease: quarantine as a control measure,” International Journal of Advanced Scientific Engineering and Technological Research, vol. 1, no. 2, pp. 34–44, 2012.
  • J. Liu, “Threshold dynamics for a HFMD epidemic model with periodic transmission rate,” Nonlinear Dynamics, vol. 64, no. 1-2, pp. 89–95, 2011.
  • X. Wang and Y. Xue, “Analysis of HFMD in China using a SEIQR model,” Far East Journal of Mathematical Sciences, vol. 58, no. 1, pp. 83–98, 2011.
  • J.-Y. Yang, Y. Chen, and F.-Q. Zhang, “Stability analysis and optimal control of a hand-foot-mouth disease (HFMD) model,” Journal of Applied Mathematics and Computing, vol. 41, no. 1-2, pp. 99–117, 2013.
  • Y. Ma, M. Liu, Q. Hou, and J. Zhao, “Modelling seasonal HFMD with the recessive infection in Shandong, China,” Mathematical Biosciences and Engineering, vol. 10, no. 4, pp. 1159–1171, 2013.
  • Y. Zhu, B. Xu, X. Lian, W. Lin, Z. Zhou, and W. Wang, “A hand-foot-and-mouth disease model with periodic transmission rate in Wenzhou, China,” Abstract and Applied Application, 2014.
  • L. W. Ang, B. K. Koh, K. P. Chan, L. T. Chua, L. James, and K. T. Goh, “Epidemiology and control of hand, foot and mouth disease in Singapore,” Annals of the Academy of Medicine Singapore, vol. 38, no. 2, pp. 106–112, 2009.
  • S. Blomqvist, P. Klemola, S. Kaijalainen et al., “Co-circulation of coxsackieviruses A6 and A10 in hand, foot and mouth disease outbreak in Finland,” Journal of Clinical Virology, vol. 48, no. 1, pp. 49–54, 2010.
  • E. Ma, T. Lam, K. C. Chan, C. Wong, and S. K. Chuang, “Changing epidemiology of hand, foot, and mouth disease in Hong Kong, 2001–2009,” Japanese Journal of Infectious Diseases, vol. 63, no. 6, pp. 422–426, 2010.
  • L.-X. Mao, B. Wu, W.-X. Bao et al., “Epidemiology of hand, foot, and mouth disease and genotype characterization of Enterovirus 71 in Jiangsu, China,” Journal of Clinical Virology, vol. 49, no. 2, pp. 100–104, 2010.
  • S. S. Y. Wong, C. C. Y. Yip, S. K. P. Lau, and K. Y. Yuen, “Human enterovirus 71 and hand, foot and mouth disease,” Epidemiology and Infection, vol. 138, no. 8, pp. 1071–1089, 2010.
  • Y. L. Hii, J. Rocklöv, and N. Ng, “Short term effects of weather on Hand, foot and mouth disease,” PLoS ONE, vol. 6, no. 2, Article ID e16796, 2011.
  • J.-F. Wang, Y.-S. Guo, G. Christakos et al., “Hand, foot and mouth disease: spatiotemporal transmission and climate,” International Journal of Health Geographics, vol. 10, article 25, 2011.
  • Q. Zhu, Y. Hao, J. Ma, S. Yu, and Y. Wang, “Surveillance of hand, foot, and mouth disease in Mainland China (2008-2009),” Biomedical and Environmental Sciences, vol. 24, no. 4, pp. 349–356, 2011.
  • X. Zou, X. Zhang, B. Wang, and Y. Qiu, “Etiologic and epidemiologic analysis of hand, foot, and mouth disease in Guangzhou city: a review of 4,753 cases,” The Brazilian Journal of Infectious Diseases, vol. 16, no. 5, pp. 457–465, 2012.
  • J. P. Lott, K. Liu, and M. Landry, “Atypical hand-foot-and-mouth disease associated with coxsackievirus A6 infection,” Journal of the American Academy of Dermatology, vol. 69, no. 5, pp. 736–741, 2013.
  • M. Zeng, Y.-F. Li, X.-H. Wang et al., “Epidemiology of hand, foot, and mouth disease in children in Shanghai 2007–2010,” Epidemiology and Infection, vol. 140, no. 6, article 1122, 2012.
  • D. Zhu, X. Zhao, and X. Y. Yao, “A new factor influencing pathogen detection by molecular assay in children with both mild and severe hand, foot, and mouth disease,” Diagnostic Microbiology and Infectious Disease, vol. 76, pp. 162–167, 2013.
  • T. Deng, Y. Huang, S. Yu et al., “Spatial-temporal clusters and risk factors of hand, foot, and mouth disease at the district level in Guangdong province, China,” PloS ONE, vol. 8, no. 2, Article ID e56943, 2013.
  • J. Wang, C. Xu, S. Tong, H. Chen, and W. Yang, “Spatial dynamic patterns of handfoot-mouth disease in the People's Republic of China,” Geospatial Health, vol. 7, no. 2, pp. 381–390, 2013.
  • Wenzhou City Population and Family Planning Commis-sion, “A survey of wenzhou population,” (Chinese), http://www.wzrkjs.gov.cn/.
  • M. Porta, A Dictionary of Epidemiology, Oxford University Press, New York, NY, USA, fifth edition, 2008.
  • J. Besag, J. York, and A. Mollié, “Bayesian image restoration, with two applications in spatial statistics,” Annals of the Institute of Statistical Mathematics, vol. 43, no. 1, pp. 1–59, 1991.
  • J. Besag and C. Kooperberg, “On conditional and intrinsic autoregressions,” Biometrika, vol. 82, no. 4, pp. 733–746, 1995.
  • A. B. Lawson, Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2009.
  • P. E. Pfeifer and S. J. Deutsch, “A three-stage iterative procedure for space-time modeling,” Technometrics, vol. 22, no. 1, pp. 35–47, 1980.
  • C. A. Glasbey and D. J. Allcroft, “A spatiotemporal auto-regressive moving average model for solar radiation,” Journal of the Royal Statistical Society C, vol. 57, no. 3, pp. 343–355, 2008.
  • J. D. Cryer and K. S. Cha, Time Series Analysis with Applications in R, Springer, 2008.
  • J. G. Ibrahim and M.-H. Chen, “Power prior distributions for regression models,” Statistical Science, vol. 15, no. 1, pp. 46–60, 2000.
  • W. R. Gilks and P. Wild, “Adaptive rejection sampling for gibbs samlping,” Applied Statistics, vol. 41, pp. 337–348, 1992.
  • H. Akaike, “A new look at the statistical model identification,” IEEE Transactions on Automatic Control, vol. 19, pp. 716–723, 1974.
  • L.-H. Cao, M. Ren, P.-L. Zhao, J.-B. Ma, S.-L. Sun, and J.-S. Dong, “A exploration and study of the relationships of hand-foot-mouth disease (HFMD) and the climate,” Chinese Journal of Experimental and Clinical Virology, vol. 25, no. 3, pp. 227–229, 2011.
  • D. Onozuka and M. Hashizume, “The influence of temperature and humidity on the incidence of hand, foot, and mouth disease in Japan,” Science of the Total Environment, vol. 410-411, pp. 119–125, 2011. \endinput