基于免疫应答和药物治疗的艾滋病病毒动力学模型与研究

HIV specific cytotoxic T lymphocyte immune response is closely related to the inhibition of viral replication and disease progression, which plays a very important role in the control of viral infection. In this project, based on the HIV pathogenesis and viral immunology, we will formulate some dynamical models which can describe the interaction between viral load, CD4+ T-cells, immune response and drug treatment, and will show the dynamical behavior of these models. Using the estimated data of the medical literatures and sensitivity analysis method, we are trying to find the key parameters of the model, and estimate these parameter values. Then, we analyze the dynamical model theoretically and simulate the disease tendency numerically. We explore the effect of varying the combination drug efficacy on model behavior, and the possibility of reconstituting the immune response through antiretroviral therapy. Compared to HIV models of immune response with or without drug resistance, we find substantial difference between them. Furthermore, the impact of target cell density function is studied on models behavior.

HIV特异性细胞毒性T淋巴细胞免疫应答对抑制病毒的复制和疾病的进展有着密切的关系，在控制病毒感染方面起着十分重要的作用。项目将针对艾滋病病毒的发病机理和微观免疫学原理，建立描述感染后艾滋病病毒、CD4+T 细胞、免疫应答和药物治疗相互作用的动力学模型，并研究模型的动力学性态；利用医学文献中已有数据，运用敏感性分析方法找到决定模型的关键参数，并进行参数估计，对模型进行理论分析和计算机模拟；分析联合药物药效的改变对模型动力学行为的影响，并探讨通过抗逆转录病毒治疗免疫应答重建的可能性．比较考虑耐药性因素和不考虑耐药性因素情况下免疫应答模型的异同点，分析不同性质的CD4+ T 细胞密度相关函数对模型动力学性态的影响。

本项目针对艾滋病病毒的发病机理和药物治疗过程中耐药性因素，建立了一类具有一般形式的健康 T 细胞、药物治疗、耐药性和细胞内时滞的 HIV 病毒动力学模型。首先，给出了确定感染平衡点存在与否的两个基本再生数：具有敏感株和耐药株的基本再生数。通过构造 Lyapunov 函数，得到了未感染平衡点和仅有耐药株存在的平衡点的全局渐近稳定性。理论上，我们还讨论了感染平衡点的局部渐近稳定性，并进一步探讨了具有不同性质的 CD4+ T 细胞密度函数对感染平衡点稳定性的影响。运用数值模拟，我们讨论了 CD4+ T 细胞密度和细胞内的时滞对模型动力学行为的影响。