A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in china.

## Mathematics

### Journal of Applied & Computational Mathematics

Author(s): Zhao S, Xu Z, Lu Y

Abstract BACKGROUND: Before universal infant immunization against hepatitis B virus (HBV) in 1986 China was a region endemic for HBV infection. The prevalence of HBV infection in the population was about 60\% and the proportion of chronic HBV carriers around 10\%. These HBV carriers could progress to chronic hepatitis B, cirrhosis, and primary hepatocellular carcinoma. Since 1976, large-scale sero-surveys of HBV infection have been carried out and a lot of data have been collected. METHOD: This paper describes a mathematical model developed to predict the dynamics of HBV transmission and to evaluate the long-term effectiveness of the vaccination programme. We used a compartment model expressed by a set of partial differential equations based on the characteristics of HBV infection. RESULTS: All parameters, expressed in the model as a non-linear function of age and time since vaccination, were estimated using sero-survey data. The model fits well with both pre-vaccination and post-vaccination sero-surveys. The observed and estimated age-specific prevalence rates of HBV infection and HBV carriage agree with each other. According to our model, if all newborns are vaccinated according to schedule, the rate of HBV carriage will decline sharply over time to 0.2\% in 70 years. By then, the ratio of acute hepatitis B will be less than 0.5\% and the ratio of chronic hepatitis B will be around 5\%. CONCLUSIONS: The results suggest that HBV infection in China can be controlled in just one generation, and eventually eliminated. Our model shows that vaccination coverage is the most important indicator for the elimination of HBV transmission. The higher the vaccination coverage, the better the long-term effectiveness of immunization. Thus, the key to controlling and eliminating HBV transmission in China is to find ways to immunize all infants throughout the country, especially in poor, rural areas.
This article was published in Int J Epidemiol and referenced in Journal of Applied & Computational Mathematics

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