Abstract and Applied Analysis

A Hand-Foot-and-Mouth Disease Model with Periodic Transmission Rate in Wenzhou, China

Yeting Zhu, Boyang Xu, Xinze Lian, Wang Lin, Zumu Zhou, and Weiming Wang

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Abstract

We establish an SEIQRS epidemic model with periodic transmission rate to investigate the spread of seasonal HFMD in Wenzhou. The value of this study lies in two aspects. Mathematically, we show that the global dynamics of the HFMD model can be governed by its reproduction number R 0 ; if R 0 < 1 , the disease-free equilibrium of the model is globally asymptotically stable, which means that the disease will vanish after some period of time; while if R 0 > 1 , the model has at least one positive periodic solution and is uniformly persistent, which indicates that HFMD becomes an endemic disease. Epidemiologically, based on the statistical data of HFMD in Wenzhou, we find that the HFMD becomes an endemic disease and will break out in Wenzhou. One of the most interesting findings is that, for controlling the HFMD spread, we must increase the quarantined rate or decrease the treatment cycle.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 234509, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273271

Digital Object Identifier
doi:10.1155/2014/234509

Mathematical Reviews number (MathSciNet)
MR3191026

Zentralblatt MATH identifier
07021962

Citation

Zhu, Yeting; Xu, Boyang; Lian, Xinze; Lin, Wang; Zhou, Zumu; Wang, Weiming. A Hand-Foot-and-Mouth Disease Model with Periodic Transmission Rate in Wenzhou, China. Abstr. Appl. Anal. 2014 (2014), Article ID 234509, 11 pages. doi:10.1155/2014/234509. https://projecteuclid.org/euclid.aaa/1412273271


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References

  • Centers for Disease Control and Prevention, “About hand, foot, and mouth disease,” http://www.cdc.gov/hand-foot-mouth.
  • J. P. Lott, K. Liu, M. Landry et al., “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.
  • 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.
  • 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.
  • 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.
  • 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, pp. 1122–1130, 2012.
  • 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, 2001–2007,” 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • D. Zhu, X. Zhao, Y. Yao et al., “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, no. 2, pp. 162–167, 2013.
  • F. C. 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.
  • 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.
  • H. Ni, B. Yi, J. Yin et al., “Epidemiological and etiological characteristics of hand, foot, and mouth disease in Ningbo, China, 2008–2011,” Journal of Clinical Virology, vol. 54, no. 4, pp. 342–348.
  • J. Ma and Z. Ma, “Epidemic threshold conditions for seasonally forced SEIR models,” Mathematical Biosciences and Engineering, vol. 3, no. 1, pp. 161–172, 2006.
  • J. Dushoff, J. B. Plotkin, S. A. Levin, and D. J. D. Earn, “Dynamical resonance can account for seasonality of influenza epidemics,” Proceedings of the National Academy of Sciences of the United States of America, vol. 101, no. 48, pp. 16915–16916, 2004.
  • Wenzhou City Population and Family Planning Commission, “A survey of wenzhou population,” http://www.wzrkjs.gov.cn, (in Chinese).
  • Zhejiang Online Source for Disease Control and Prevention, “The statistic results of “Ten legal infectious diseases” in Zhejiang province in 2012,” http://www.cdc.zj.cn, (in Chinese).
  • D. Xiao and S. Ruan, “Global analysis of an epidemic model with nonmonotone incidence rate,” Mathematical Biosciences, vol. 208, no. 2, pp. 419–429, 2007.
  • G. Aronsson and R. B. Kellogg, “On a differential equation arising from compartmental analysis,” Mathematical Biosciences, vol. 38, no. 1-2, pp. 113–122, 1978.
  • M. W. Hirsch, “Systems of differential equations that are competitive or cooperative. II. Convergence almost everywhere,” SIAM Journal on Mathematical Analysis, vol. 16, no. 3, pp. 423–439, 1985.
  • H. L. Smith and P. Waltman, The Theory of the Chemostat, vol. 13 of Cambridge Studies in Mathematical Biology, Cambridge University Press, Cambridge, UK, 1995.
  • F. Zhang and X.-Q. Zhao, “A periodic epidemic model in a patchy environment,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 496–516, 2007.
  • N. Bacaër and S. Guernaoui, “The epidemic threshold of vector-borne diseases with seasonality. The case of cutaneous leishmaniasis in Chichaoua, Morocco,” Journal of Mathematical Biology, vol. 53, no. 3, pp. 421–436, 2006.
  • W. Wang and X.-Q. Zhao, “Threshold dynamics for compartmental epidemic models in periodic environments,” Journal of Dynamics and Differential Equations, vol. 20, no. 3, pp. 699–717, 2008.
  • L. Perko, Differential Equations and Dynamical Systems, Springer, New York, NY, USA, 2000.
  • X.-Q. Zhao, Dynamical Systems in Population Biology, Springer, New York, NY, USA, 2003.
  • 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. \endinput