In this paper, we investigate the global properties of two general models of pathogen infection with immune deficiency. Both pathogen-to-cell and cell-to-cell transmissions are considered. Latently infected cells are included in the second model. We show that the solutions are nonnegative and bounded. Lyapunov functions are organized to prove the global asymptotic stability for uninfected and infected steady states of the models. Analytical expressions for the basic reproduction number $\mathcal{R}_{0}$ and the necessary condition under which the uninfected and infected steady states are globally asymptotically stable are established. We prove that if $\mathcal{R}_{0}$ < 1 then the uninfected steady state is globally asymptotically stable (GAS), and if $\mathcal{R}_{0}$ > 1 then the infected steady state is GAS. Numerical simulations are performed and used to support the analytical results.

中文翻译：

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具有两种免疫缺陷的传染传播的一般病原体动力学模型的稳定性

在本文中，我们研究了两种免疫缺陷病原体感染的通用模型的全局特性。病原体到细胞和细胞到细胞的传播都被考虑了。潜伏感染的细胞包括在第二个模型中。我们证明了解是非负的和有界的。组织Lyapunov函数以证明模型的未感染和感染稳态的全局渐近稳定性。建立了基本繁殖数$ \ mathcal {R} _ {0} $的解析表达式，以及未感染和被感染的稳态全局渐近稳定的必要条件。我们证明如果$ \ mathcal {R} _ {0} $ <1则未感染的稳态为全局渐近稳定（GAS），如果$ \ mathcal {R} _ {0} $> 1则被感染的稳态是GAS。