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 R 0, 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 R 0 in terms of various model parameters. Moreover, we demonstrate that it is more reasonable to regard R 0 rather than the average basic reproduction number R̄ 0 or the basic reproduction number R̂ 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1226-1251 |
| Number of pages | 26 |
| Journal | Bulletin of Mathematical Biology |
| Volume | 74 |
| Issue number | 5 |
| DOIs | |
| State | Published - May 2012 |
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Keywords
- Basic reproduction number
- Periodic solution
- Rabies
- SEIRS model
- Vaccination
ASJC Scopus subject areas
- Neuroscience(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Pharmacology
- Immunology
- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)
- Environmental Science(all)
Cite this
Modeling Seasonal Rabies Epidemics in China. / Zhang, Juan; Jin, Zhen; Sun, Gui Quan; Sun, Xiang Dong; Ruan, Shigui.
In: Bulletin of Mathematical Biology, Vol. 74, No. 5, 05.2012, p. 1226-1251.Research output: Contribution to journal › Article
}
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
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 R 0, 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 R 0 in terms of various model parameters. Moreover, we demonstrate that it is more reasonable to regard R 0 rather than the average basic reproduction number R̄ 0 or the basic reproduction number R̂ 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.
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 R 0, 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 R 0 in terms of various model parameters. Moreover, we demonstrate that it is more reasonable to regard R 0 rather than the average basic reproduction number R̄ 0 or the basic reproduction number R̂ 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.
KW - Basic reproduction number
KW - Periodic solution
KW - Rabies
KW - SEIRS model
KW - Vaccination
UR - http://www.scopus.com/inward/record.url?scp=84862803655&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84862803655&partnerID=8YFLogxK
U2 - 10.1007/s11538-012-9720-6
DO - 10.1007/s11538-012-9720-6
M3 - Article
VL - 74
SP - 1226
EP - 1251
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
SN - 0092-8240
IS - 5
ER -