In this paper, dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated. The model involves the concentrations of uninfected cells, infected cells, free virus, CTL response cells, and antibody antibody response cells. There are three delays in the model: the intracellular delay, virus replication delay and the antibody delay. The basic reproductive number of viral infection, the antibody immune reproductive number, the CTL immune reproductive number, the CTL immune competitive reproductive number and the antibody immune competitive reproductive number are derived. By means of Lyapunov functionals and LaSalle’s invariance principle, sufficient conditions for the stability of each equilibrium is established. The results show that the intracellular delay and virus replication delay do not impact upon the stability of each equilibrium, but when the antibody delay is positive, Hopf bifurcation at the antibody response and the interior equilibrium will exist by using the antibody delay as a bifurcation parameter. Numerical simulations are carried out to justify the analytical results.

本文研究了具有CTL免疫反应和抗体免疫反应的HIV延迟感染模型的动力学分析。该模型涉及未感染细胞，感染细胞，游离病毒，CTL反应细胞和抗体抗体反应细胞的浓度。该模型有三个延迟：细胞内延迟，病毒复制延迟和抗体延迟。推导了病毒感染的基本生殖数，抗体免疫生殖数，CTL免疫生殖数，CTL免疫竞争生殖数和抗体免疫竞争生殖数。利用Lyapunov泛函和LaSalle不变性原理，为每个平衡的稳定性建立了充分的条件。结果表明，细胞内延迟和病毒复制延迟不影响每个平衡的稳定性，但是当抗体延迟为正时，将抗体延迟作为分叉参数，将在抗体反应和内部平衡中存在霍普夫分叉。 。进行数值模拟以证明分析结果的合理性。