Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O. Box 146, Mohammedia, Morocco.
Comput Math Methods Med. 2019 Nov 16;2019:7673212. doi: 10.1155/2019/7673212. eCollection 2019.
In this paper, a mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with adaptive immune response is presented and studied. The mathematical model includes six nonlinear differential equations describing the interaction between the uninfected cells, the exposed cells, the actively infected cells, the free viruses, and the adaptive immune response. The considered adaptive immunity will be represented by cytotoxic T-lymphocytes cells (CTLs) and antibodies. First, the global stability of the disease-free steady state and the endemic steady states is established depending on the basic reproduction number , the CTL immune response reproduction number , the antibody immune response reproduction number , the antibody immune competition reproduction number , and the CTL immune response competition reproduction number . On the other hand, different numerical simulations are performed in order to confirm numerically the stability for each steady state. Moreover, a comparison with some clinical data is conducted and analyzed. Finally, a sensitivity analysis for is performed in order to check the impact of different input parameters.
本文提出并研究了一个描述人类免疫缺陷病毒 (HIV) 发病机制和适应性免疫反应的数学模型。该数学模型包括六个非线性微分方程，描述了未感染细胞、暴露细胞、活跃感染细胞、游离病毒和适应性免疫反应之间的相互作用。所考虑的适应性免疫将由细胞毒性 T 淋巴细胞 (CTL) 和抗体来表示。首先，根据基本繁殖数 、CTL 免疫反应繁殖数 、抗体免疫反应繁殖数 、抗体免疫竞争繁殖数 和 CTL 免疫反应竞争繁殖数 ，建立了无病平衡点和地方病平衡点的全局稳定性。另一方面，进行了不同的数值模拟，以数值确认每个平衡点的稳定性。此外，还进行了与一些临床数据的比较和分析。最后，对 进行了敏感性分析，以检查不同输入参数的影响。
