Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, P.R. China.
Bull Math Biol. 2010 Aug;72(6):1492-505. doi: 10.1007/s11538-010-9503-x. Epub 2010 Jan 21.
The dynamics of a general in-host model with intracellular delay is studied. The model can describe in vivo infections of HIV-I, HCV, and HBV. It can also be considered as a model for HTLV-I infection. We derive the basic reproduction number R0 for the viral infection, and establish that the global dynamics are completely determined by the values of R0. If R0 < or = 1, the infection-free equilibrium is globally asymptotically stable, and the virus are cleared. If R0 > 1, then the infection persists and the chronic-infection equilibrium is locally asymptotically stable. Furthermore, using the method of Lyapunov functional, we prove that the chronic-infection equilibrium is globally asymptotically stable when R0 > 1. Our results shows that for intercellular delays to generate sustained oscillations in in-host models it is necessary have a logistic mitosis term in target-cell compartments.
研究了具有细胞内时滞的总体宿主模型的动力学。该模型可以描述 HIV-I、HCV 和 HBV 的体内感染，也可以被认为是 HTLV-I 感染的模型。我们推导出了病毒感染的基本繁殖数 R0，并确定了病毒的全局动力学完全由 R0 的值决定。如果 R0 <= 1，则感染无平衡点是全局渐近稳定的，病毒被清除。如果 R0 > 1，则感染持续存在，慢性感染平衡点是局部渐近稳定的。此外，我们使用李雅普诺夫函数的方法证明了当 R0 > 1 时，慢性感染平衡点是全局渐近稳定的。我们的结果表明，为了使细胞间延迟在宿主模型中产生持续的振荡，有必要在靶细胞区室中具有逻辑分裂项。
