Multiple Stable Periodic Oscillations in a Mathematical Model of CTL Response to HTLV-I Infection
Multiple Stable Periodic Oscillations in a Mathematical Model of CTL Response to HTLV-I Infection
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DOI：
10.1007/s11538-010-9591-7
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发表时间：
2011-08
影响因子：
3.5
通讯作者：
Michael Y. Li;Hongying Shu
中科院分区：
文献类型：
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作者：
Michael Y. Li;Hongying Shu
稳定的周期性振荡已被证明存在于CTL对HTLV-I感染的反应的数学模型中。这些周期性振荡可以是受感染的靶CD 4+细胞的有丝分裂、一般形式的应答函数或CTL应答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，在CTL响应HTLV-I感染的过程中的时间延迟，可以导致多个稳定的周期性的解决方案，这在振幅和周期不同的共存，与自己的盆地的吸引力。结果表明，CTL免疫应答与HTLV-I感染之间的动态相互作用是非常复杂的，CTL免疫应答动力学中的多稳定性可能以稳定振荡共存的形式存在，而不是稳定平衡点。在生物学上，我们的研究结果意味着不同的病毒感染途径或初始剂量可能导致定量和定性的不同结果。
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.