TY - JOUR
T1 - Modeling Seasonal Rabies Epidemics in China
AU - Zhang, Juan
AU - Jin, Zhen
AU - Sun, Gui Quan
AU - Sun, Xiang Dong
AU - Ruan, Shigui
N1 - Funding Information:
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.
PY - 2012/5
Y1 - 2012/5
N2 - 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 R̄0 or the basic reproduction number R̂0 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.
AB - 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 R̄0 or the basic reproduction number R̂0 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.
KW - Basic reproduction number
KW - Periodic solution
KW - Rabies
KW - SEIRS model
KW - Vaccination
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U2 - 10.1007/s11538-012-9720-6
DO - 10.1007/s11538-012-9720-6
M3 - Article
C2 - 22383117
AN - SCOPUS:84862803655
VL - 74
SP - 1226
EP - 1251
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
SN - 0092-8240
IS - 5
ER -