一类带logistic增长乙型肝炎病毒模型的稳定性和Hopf分支

Stability and Hopf bifurcation of a hepatitis B viral infection model with logistic hepatocyte growth

目前大部分感染HBV模型提出的假设是肝细胞以一个比例常数增殖和感染采用双线性发生率,考虑健康肝细胞采用logistic增长而非常数比例注入,在感染方面用标准发生率替代双线性发生率,主要讨论了无病平衡点和地方平衡点的稳定性.当基本再生数R0小于1,无病平衡点是稳定的,当R0大于1,该系统可能收敛于地方平衡点,有规律的震荡或者趋近于原点,进一步证实产生了一个Hopf分支点.

Most previous HBV infection models assume that hepatocytes regenerate at a constant rate and that the infection takes place via a mass action process. This paper replaces the constant infusion of healthy hepatocytes with a logistic growth term and the mass action infection term by a standard incidence function, and studies the stability of disease free and endemic equilibrium. When the basic reproduction number R0, is less than 1, the disease free steady state is stable, and when Ro 〉 1 the system can either converge to the chronic steady state, experience sustained oscillations, or approach the origin, a Hopf bifurcation point is identified.