一类考虑抗体免疫反应具有饱和传染率的病毒动力学模型

摘要

The Lyapunov function and the Hurwitz criterion were mainly used to prove the global and local stability of virus dynamics model which have overall infectious with immune response. It was proved that the virus was cleared if the basic reproduction number was R0≤1, and the virus persisted in the host if Ir0≤1; further, positive solutions of the model approached to an immune-free steady state if the immune response reproductive number was R1≤1, and the system tended to an endemic steady state if Ir1≤1.%主要用Lyapunov函数和Hurwitz判据去证明一类考虑抗体免疫反应具有饱和传染率的病毒动力学模型全局性及其局部稳定性.证明了当基本再生数R0≤1时,病毒最终会在宿主体内消失；而当基本再生数R0＞1时,病毒会在宿主体内存活.存活方式取决于抗体免疫再生数,如果抗体免疫再生数R1≤1,系统最终趋向于无免疫平衡点；如果免疫再生数R1＞1,系统最终趋向于正平衡点.