Title: Dynamical analysis of an HIV infection model including quiescent cells and immune response Show Chinese title

Title: HIV感染模型的动力学分析包括静息细胞和免疫反应

Abstract: This research gives a thorough examination of an HIV infection model that includes quiescent cells and immune response dynamics in the host. The model, represented by a system of ordinary differential equations, captures the complex interaction between the host's immune response and viral infection. The study focuses on the model's fundamental aspects, such as equilibrium analysis, computing the basic reproduction number $\mathcal{R}_0$, stability analysis, bifurcation phenomena, numerical simulations, and sensitivity analysis. The analysis reveals both an infection equilibrium, which indicates the persistence of the illness, and an infection-free equilibrium, which represents disease control possibilities. Applying matrix-theoretical approaches, stability analysis proved that the infection-free equilibrium is both locally and globally stable for $\mathcal{R}_0 < 1$. For the situation of $\mathcal{R}_0 > 1$, the infection equilibrium is locally asymptotically stable via the Routh--Hurwitz criterion. We also studied the uniform persistence of the infection, demonstrating that the infection remains present above a positive threshold under certain conditions. The study also found a transcritical forward-type bifurcation at $\mathcal{R}_0 = 1$, indicating a critical threshold that affects the system's behavior. The model's temporal dynamics are studied using numerical simulations, and sensitivity analysis identifies the most significant variables by assessing the effects of parameter changes on system behavior. Show Chinese abstract

Abstract: 这项研究对一个包含静止细胞和宿主体内免疫反应动力学的HIV感染模型进行了全面的考察。 该模型由一组常微分方程表示，捕捉了宿主免疫反应与病毒感染之间的复杂相互作用。 本研究关注模型的基本方面，如平衡点分析、计算基本再生数$\mathcal{R}_0$、稳定性分析、分岔现象、数值模拟和敏感性分析。 分析结果显示了一个感染平衡点，表明疾病持续存在，以及一个无感染平衡点，代表疾病控制的可能性。 应用矩阵理论方法，稳定性分析证明当$\mathcal{R}_0 < 1$时，无感染平衡点在局部和全局上都是稳定的。 对于$\mathcal{R}_0 > 1$的情况，通过 Routh--Hurwitz 准则证明感染平衡点是局部渐近稳定的。 我们还研究了感染的均匀持久性，证明在某些条件下，感染会在正阈值以上持续存在。 研究还发现，在$\mathcal{R}_0 = 1$处出现了一种跨临界前向型分岔，表明一个影响系统行为的关键阈值。 通过数值模拟研究了模型的时间动力学，并通过敏感性分析识别了最重要的变量，评估参数变化对系统行为的影响。