中文摘要：

建立具有Holling Ⅱ感染率且考虑免疫应答的HIV模型,讨论系统解的非负性和有界性,得到确定模型动力学性态的基本再生数,最后通过分析模型在平衡点处相应的特征方程,利用微分方程基本理论,证明模型在正平衡点处是局部渐近稳定的。即人类免疫缺陷病毒HIV将在个体体内持续存在,并且免疫应答会持续起作用,并用数值模拟验证结果。

英文摘要：

A HIV model with Holling Ⅱinfection rate and immune response is built. Then the nonnegativity and boundedness of the solution are discussed,and the basic reproduction number which determines the dynamical behaviors of the infection model is obtained. Finally,by analyzing corresponding characteristic equation at the positive equilibrium,it is proven that the positive equilibrium is locally asymptotically stable. That is,Human Immunodeficiency Virus（ HIV） persists in body of the infected individuals,and numerical simulations are carried out to support the result.