Bulletin of Mathematical Biology

, Volume 74, Issue 5, pp 1226–1251 | Cite as

Modeling Seasonal Rabies Epidemics in China

  • Juan Zhang
  • Zhen Jin
  • Gui-Quan Sun
  • Xiang-Dong Sun
  • Shigui Ruan
Original Article

Abstract

Human rabies, an infection of the nervous system, is a major public-health problem in China. In the last 60 years (1950–2010) there had been 124,255 reported human rabies cases, an average of 2,037 cases per year. However, the factors and mechanisms behind the persistence and prevalence of human rabies have not become well understood. The monthly data of human rabies cases reported by the Chinese Ministry of Health exhibits a periodic pattern on an annual base. The cases in the summer and autumn are significantly higher than in the spring and winter. Based on this observation, we propose a susceptible, exposed, infectious, and recovered (SEIRS) model with periodic transmission rates to investigate the seasonal rabies epidemics. We evaluate the basic reproduction number R0, analyze the dynamical behavior of the model, and use the model to simulate the monthly data of human rabies cases reported by the Chinese Ministry of Health. We also carry out some sensitivity analysis of the basic reproduction number R0 in terms of various model parameters. Moreover, we demonstrate that it is more reasonable to regard R0 rather than the average basic reproduction number \(\bar{R}_{0}\) or the basic reproduction number \(\hat{R}_{0}\) of the corresponding autonomous system as a threshold for the disease. Finally, our studies show that human rabies in China can be controlled by reducing the birth rate of dogs, increasing the immunization rate of dogs, enhancing public education and awareness about rabies, and strengthening supervision of pupils and children in the summer and autumn.

Keywords

Rabies SEIRS model Basic reproduction number Periodic solution Vaccination 

Notes

Acknowledgements

The research was partially supported by the National Natural Science Foundation of China (11171314, 11147015 and 10901145), Program for Basic Research (2010011007), International and Technical Cooperation Project (2010081005) and Bairen Project of Shan’xi Province, and the National Science Foundation of USA (DMS-1022728). The authors would like to thank Dr. Luju Liu for her help on using the Matlab program. The authors are also grateful to the referees for their helpful comments and suggestions.

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Copyright information

© Society for Mathematical Biology 2012

Authors and Affiliations

  • Juan Zhang
    • 1
  • Zhen Jin
    • 1
  • Gui-Quan Sun
    • 1
  • Xiang-Dong Sun
    • 2
  • Shigui Ruan
    • 3
  1. 1.Department of MathematicsNorth University of ChinaTaiyuanPeople’s Republic of China
  2. 2.The Laboratory of Animal Epidemiological SurveillanceChina Animal Health and Epidemiology CenterQingdaoPeople’s Republic of China
  3. 3.Department of MathematicsUniversity of MiamiCoral GablesUSA

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