一类具有饱和感染率和胞内时滞的病毒感染模型的稳定性和Hopf分支

Stability and Hopf Bifurcation of a Class of Viral Infection Model with Saturation Infective Rate and Intracellular Delay

本文研究一类具有饱和感染率以及胞内时滞的病毒感染模型.通过计算,得到模型的基本再生数.通过构造适当的Lyapunov函数,利用La Salle不变原理,证明当基本再生数小于1时,未感染平衡点是全局渐近稳定的;当基本再生数大于1时,得到病毒感染平衡点全局渐近稳定的充分条件.利用分支理论,证明当τ=τ^＊时,系统在病毒感染平衡点处存在Hopf分支.

In this paper,we propose a class of viral infection model with a saturation infective rate and intracellular delay.By calculation,we derive the reproduction number.By constructing suitable Lyapunov functionals and using La Salle＇s invariance principle,we prove that when the reproduction number for viral infection is less than unity,the infection-free equilibrium is globally asymptotically stable.When the reproduction number for viral infection is greater than unity,a sufficient condition for proving the global stability of the viral infection equilibrium is derived.By bifurcation theory,we prove that the system will undergo a Hopf bifurcation at viral infection equilibrium when τ = τ~＊.