In this paper, we develop mathematical models that include impairment of B-cell functions in order to study HIV dynamics. Two forms of the incidence rate have been considered, bilinear and general nonlinear. Three types of infected cells have been incorporated into the models, namely latently infected, short-lived productively infected and long-lived productively infected. The models have at most two equilibria, whose existence is characterized by means of the basic reproduction number [Formula: see text]. The global stability of each equilibrium is proven by using the Lyapunov method. The effects of impairment of B-cell functions and of antiviral treatment on the human immunodeficiency virus (HIV) dynamics are studied. We have shown that if the functions of B-cell are impaired, then the concentration of HIV increases in the plasma. Moreover, we have determined the minimal drug efficacy which is required to reduce the concentration of HIV particles to a lower level. We have shown that a more accurate computation of drug efficacy can be performed by using our proposed model. Our theoretical results are illustrated by means of numerical simulations.

中文翻译：

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HIV 动力学模型的全球特性，包括 B 细胞功能的损害

在本文中，我们开发了包括 B 细胞功能损伤在内的数学模型，以研究 HIV 动力学。已经考虑了两种形式的发生率，双线性和一般非线性。三种类型的感染细胞已被纳入模型，即潜伏感染、短寿命有效感染和长寿命有效感染。这些模型最多有两个平衡点，它们的存在是通过基本再生数来表征的[公式：见正文]。使用李雅普诺夫方法证明了每个平衡的全局稳定性。研究了 B 细胞功能受损和抗病毒治疗对人类免疫缺陷病毒 (HIV) 动力学的影响。我们已经证明，如果 B 细胞的功能受损，那么血浆中的 HIV 浓度就会增加。而且，我们已经确定了将 HIV 颗粒浓度降低到较低水平所需的最小药物功效。我们已经表明，使用我们提出的模型可以更准确地计算药物功效。我们的理论结果通过数值模拟来说明。