This paper studies an $ (n+2) $-dimensional nonlinear HIV dynamics model that characterizes the interactions of HIV particles, susceptible CD4$ ^{+} $ T cells and $ n $-stages of infected CD4$ ^{+} $ T cells. Both virus-to-cell and cell-to-cell infection modes have been incorporated into the model. The incidence rates of viral and cellular infection as well as the production and death rates of all compartments are modeled by general nonlinear functions. We have revealed that the solutions of the system are nonnegative and bounded, which ensures the well-posedness of the proposed model. The basic reproduction number $ \Re_{0} $ is determined which insures the existence of the two equilibria of the model under consideration. A set of conditions on the general functions has been established which is sufficient to investigate the global stability of the model's equilibria. The global asymptotic stability of the two equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. We have proven that if $ \Re_{0}\leq1 $, then the infection-free equilibrium is globally asymptotically stable, and if $ \Re _{0}>1 $, then the chronic-infection equilibrium is globally asymptotically stable. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.

中文翻译：

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具有多阶段感染细胞和两种感染途径的一般 HIV 动力学模型的稳定性分析

本文研究了$(n+2)$维非线性HIV动力学模型，该模型表征了HIV粒子、易感CD4$^{+}$T细胞和$n$-受感染CD4$^{+}$阶段的相互作用T细胞。病毒到细胞和细胞到细胞的感染模式已被纳入模型。病毒和细胞感染的发生率以及所有区室的产生率和死亡率由一般非线性函数建模。我们已经揭示了系统的解是非负的和有界的，这确保了所提出模型的适定性。确定基本再生数 $ \Re_{0} $，以确保所考虑模型的两个平衡的存在。已经建立了一组关于一般函数的条件，这些条件足以研究模型平衡的全局稳定性。利用李雅普诺夫函数和拉萨尔不变性原理证明了这两个平衡点的全局渐近稳定性。我们已经证明，如果 $\Re_{0}\leq1 $，则无感染均衡全局渐近稳定，如果 $\Re_{0}>1 $，则慢性感染均衡全局渐近稳定。理论结果通过具有特定形式的一般函数的模型的数值模拟来说明。那么无感染均衡是全局渐近稳定的，如果$\Re_{0}>1$，那么慢性感染均衡是全局渐近稳定的。理论结果通过具有特定形式的一般函数的模型的数值模拟来说明。那么无感染均衡是全局渐近稳定的，如果$\Re_{0}>1$，那么慢性感染均衡是全局渐近稳定的。理论结果通过具有特定形式的一般函数的模型的数值模拟来说明。