中文摘要：

提出了一类具时滞与饱和发生率的HIV-1传染病模型,分析讨论了无病平衡点E0（T0,0,0）和正平衡点E＋（T＊,I＊,V＊）的全局稳定性。通过构造Lyapunov函数和La Salle不变集原理,证明了当dμ〉sγβ,对任意τ≥0,无病平衡点E0（T0,0,0）是全局渐近稳定的;

英文摘要：

A HIV- 1 epidemic model with time delay and saturation incidence rate is proposed. The global stabilities of a disease-free equilibrium E0（ T0,0,0） and a positive equilibrium E＋（ T＊,I＊,V＊）are discussed. By constructing Lyapunov functions and La Salle＇s invariant principle,it is shown that if dμ sγβ,the disease-free equilibrium E0（ T0,0,0） is globally asymptotically stable,and if dμ sγβ,the positive equilibrium E＋（ T＊,I＊,V＊） is globally asymptotically stable,for all τ ≥ 0. Numerical simulations are carried out to illustrate the theoretical results.