A HIV virus-to-cell dynamical model with distributed delay and Beddington-DeAngelis functional response is proposed in this paper. Using the characteristic equations and analytical means, the principle reproduction number R₀ on the local stability of infection-free and chronic-infection equilibria is established. Furthermore, by constructing suitable Lyapunov functionals and using LaSalle invariance principle, we show that if R₀ ≤ 1 the infection-free equilibrium is globally asymptotically stable, while if R₀ > 1 the chronic-infection equilibrium is globally asymptotically stable. Numerical simulations are presented to illustrate the theoretical results. Comparing the effects between discrete and distributed delays on the stability of HIV virus-to-cell dynamical models, we can see that they could be same and different even opposite.

中文翻译：

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具有Beddington-DeAngelis功能反应和分布时间延迟的一类HIV病毒-细胞动力学模型的全局稳定性

本文提出了一种具有分布式时延和Beddington-DeAngelis功能反应的HIV病毒细胞动力学模型。利用特征方程和解析方法，建立了无感染和慢性感染平衡的局部稳定性的基本繁殖数R ₀。此外，通过构造合适的Lyapunov泛函并使用LaSalle不变性原理，我们表明，如果R _0≤1，则无感染平衡是全局渐近稳定的，而如果R ₀> 1，慢性感染平衡在全局渐近稳定。数值模拟表明了理论结果。比较离散延迟和分布式延迟对HIV病毒到细胞动力学模型稳定性的影响，我们可以看到它们可以相同也可以不同甚至相反。