Wang Yan, Zhou Yicang, Brauer Fred, Heffernan Jane M
College of Science, China University of Petroleum, Qingdao, 266580, Shandong, China,
J Math Biol. 2013 Oct;67(4):901-34. doi: 10.1007/s00285-012-0580-3. Epub 2012 Aug 29.
We present two HIV models that include the CTL immune response, antiretroviral therapy and a full logistic growth term for uninfected CD4+ T-cells. The difference between the two models lies in the inclusion or omission of a loss term in the free virus equation. We obtain critical conditions for the existence of one, two or three steady states, and analyze the stability of these steady states. Through numerical simulation we find substantial differences in the reproduction numbers and the behaviour at the infected steady state between the two models, for certain parameter sets. We explore the effect of varying the combination drug efficacy on model behaviour, and the possibility of reconstituting the CTL immune response through antiretroviral therapy. Furthermore, we employ Latin hypercube sampling to investigate the existence of multiple infected equilibria.
我们提出了两种包含细胞毒性T淋巴细胞（CTL）免疫反应、抗逆转录病毒疗法以及未感染CD4 + T细胞完整逻辑斯蒂增长项的HIV模型。这两种模型的区别在于自由病毒方程中是否包含一个损失项。我们得出了存在一个、两个或三个稳态的临界条件，并分析了这些稳态的稳定性。通过数值模拟，我们发现对于某些参数集，两种模型在繁殖数和感染稳态行为方面存在显著差异。我们探讨了改变联合药物疗效对模型行为的影响，以及通过抗逆转录病毒疗法重建CTL免疫反应的可能性。此外，我们采用拉丁超立方抽样来研究多个感染平衡点的存在情况。
