一类含潜伏期和CTL免疫反应的病毒感染模型的全局渐近稳定性

Global Asymptotic Stability of a Class of Viral Infection Model with Latent Period and CTL Immune Response

研究一类具有潜伏期和CTL免疫反应的病毒感染模型.通过计算,得到决定模型全局性质的两个阈值,即病毒感染基本再生数和CTL免疫基本再生数;通过构造适当的Lyapunov函数,利用LaSalle不变性原理,证明当病毒感染基本再生数小于1时,未感染平衡点是全局渐近稳定的;当CTL免疫基本再生数小于1且病毒感染基本再生数大于1时,无免疫介导的病毒感染平衡点是全局渐近稳定的;当CTL免疫基本再生数大于1时,免疫介导的病毒感染平衡点是全局渐近稳定的.

In this paper, we propose a viral infection model with latent period and CTL immune response. By calculation, we derive two thresholds to determine the global dynamics of the model, i.e., the reproduction number for viral infection and for CTL immune response. By constructing suitable Lyapunov functionals and using LaSalle＇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 andthe reproduction number for CTL immune response is less than unity, the immune- inactivated equilibrium is globally asymptotically stable; when the reproduction num- ber for CTL immune response is greater than unity, the immune activated equilibrium is globally asymptotically stable.