一类具有病毒饱和增殖的病毒-免疫动力学模型的分析

A qualitative analysis of an virus-immune dynamical model with virus saturation proliferation

在假设病毒增殖率为Michaelis-Menten函数的基础上,提出了一类病毒增殖具有饱和性的病毒与特异性免疫细胞相互作用的模型.分析发现该模型至多有两个正平衡点并会发生鞍结点分支;借助中心流形定理讨论了平衡点的局部稳定性;运用Bendixson-Dulac定理排除了周期解的存在性,进而得到模型的全局动力学性态.数值模拟显示了病毒与免疫系统相互作用的结果对初始状态的依赖性,以及在作用过程中会出现病毒载量和免疫细胞种群数量的持续振荡.

Based on the michaelis-Menten function of virus proliferation rate, a model of interaction between specific immune cells and viruses with saturated virus proliferation was proposed. It is found that the model has at most two positive equilibria and that the saddle-node bifurcation can occur under certain conditions. The local stability of equilibria is discussed by the central manifold theorem.Bendixson-Dulac theorem is applied to eliminate the existence of periodic solutions, and the global dynamics of the model is obtained. The results of the interaction between the virus and the immune system are shown to be dependent on the initial conditions when there are two positive equilibria, and the sustained oscillations of the viral load and immune cells are possible.