Department of Mathematics, Harbin Institute of Technology, Heilongjiang, P.R. China.
Bull Math Biol. 2011 Aug;73(8):1774-93. doi: 10.1007/s11538-010-9591-7. Epub 2010 Oct 26.
Stable periodic oscillations have been shown to exist in mathematical models for the CTL response to HTLV-I infection. These periodic oscillations can be the result of mitosis of infected target CD4(+) cells, of a general form of response function, or of time delays in the CTL response. In this study, we show through a simple mathematical model that time delays in the CTL response process to HTLV-I infection can lead to the coexistence of multiple stable periodic solutions, which differ in amplitude and period, with their own basins of attraction. Our results imply that the dynamic interactions between the CTL immune response and HTLV-I infection are very complex, and that multi-stability in CTL response dynamics can exist in the form of coexisting stable oscillations instead of stable equilibria. Biologically, our findings imply that different routes or initial dosages of the viral infection may lead to quantitatively and qualitatively different outcomes.
已经在 HTLV-I 感染的 CTL 反应的数学模型中显示出稳定的周期振荡的存在。这些周期性振荡可能是受感染的靶 CD4(+)细胞有丝分裂的结果，是一般形式的反应函数的结果，或者是 CTL 反应中的时间延迟的结果。在这项研究中，我们通过一个简单的数学模型表明，CTL 对 HTLV-I 感染的反应过程中的时间延迟会导致多个稳定的周期解共存，这些解在幅度和周期上有所不同，并有各自的吸引域。我们的结果表明，CTL 免疫反应与 HTLV-I 感染之间的动态相互作用非常复杂，CTL 反应动力学中的多稳定性可以以共存的稳定振荡的形式存在，而不是稳定的平衡点。从生物学角度来看，我们的发现表明，病毒感染的不同途径或初始剂量可能导致数量和质量上不同的结果。
