一类乙肝病毒传播的动力学模型研究

The Study on Dynamical Model of HBV Infection

根据乙肝病毒性肝炎(HBV)预防接种后出现的免疫逃避现象,且这种免疫逃避因年龄段不同而出现差异,本文考虑了具有阶段结构和连续预防接种的SIRS传染病模型.此模型把人群分为幼年和成年两个阶段结构;疾病采用标准发生率,在幼年和成年群体中均可传播,且只考虑对幼年群体进行连续预防接种,进而研究这种模型的渐近性态.在连续预防接种且不考虑垂直传染的情况下,得到此传染病模型的基本再生数R0,利用Routh-Hurwitz准则分别证明无病平衡点和正平衡点的局部稳定性,并选取合适的参数进行数值模拟.

The paper probes into phenomenon of the immune escape after the vaccination of hepatitis B viral （HBV） and this immune escape is different from the age bracket. The SIRS epidemic model with stage structure and continuous vaccination is considered in this paper. In this infectious disease model, the objects are divided into two stage-structures： the infancy stage and the adult stage; the disease with standard incidence ratio in both infancy and adult groups can be transmitted and only the infancy group is considered to take the continuous vaccination, the asymptotic behavior of this model is studied thereafter. The basic reproductive number R0 of this model is obtained in the case of continuous vaccination without considering vertical infection. It is respectively through Routh-Hurwitz criterion that the local stability of the disease-free equilibrium point and the positive equilibrium point are proved. Finally, the appropriate parameters are selected for numerical simulation.