中文摘要：

本文主要研究一类抗体免疫下具有治愈率的HIV感染模型的动力学行为．该模型不仅考虑潜伏阶段的感染细胞而且潜伏期的感染细胞可以治愈转化为健康的易感细胞．通过构造Lyapunov函数，证明了在一定条件下，系统的无感染平衡点，无免疫平衡点以及感染平衡点的全局渐近稳定性．

英文摘要：

In this paper, an HIV-1 infection model with antibody immune response and cure rate is proposed and investigated. Our main purposes are that an eclipse stage for the infected cells is included and the cure of these cells is recovered to uninfected cells. The global stability of HIV-1 infection model is determined by using Lyapunov functions for infection-free equilibrium, immune-free equilibrium and infected equilibrium when some conditions hold.