A mathematical model of HIV infection with the combination of drug therapy including cytotoxic T-lymphocyte (CTL) and the antibody immune response is examined. The threshold value represented as the basic reproduction ratio $R_{0}$ is derived. This reveals that $R_{0} < 1$ is locally asymptotically stable in the viral free steady state, and the infected steady state condition remains locally asymptotically stable with $R_{0} > 1$ in the absence of a delay in the immune response. Moreover, the existence of Hopf bifurcation with CTL response delay is demonstrated. The estimation of delay length is used to maintain stability. Numerical simulations are implemented to explain the mathematical results.

中文翻译：

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非线性HIV感染模型的Hopf分叉分析及药物治疗对延迟免疫反应的影响

结合药物疗法（包括细胞毒性T淋巴细胞（CTL））和抗体免疫反应，研究了HIV感染的数学模型。导出表示为基本再现率$ R_ {0} $的阈值。这表明$ R_ {0} <1 $在无病毒的稳定状态下是局部渐近稳定的，在没有免疫延迟的情况下，受感染的稳定状态在$ R_ {0}> 1 $的情况下仍保持局部渐近稳定。响应。此外，证明了存在具有CTL响应延迟的Hopf分叉。延迟长度的估计用于维持稳定性。进行数值模拟以解释数学结果。