胸腺细胞发育非线性模型的稳定性分析

T细胞同祖细胞在骨髓中的发育一样在胸腺中分裂、分化、并最终发育成为成熟的T细胞.研究人员通过建立一类描述T细胞增殖、分化、死亡的微分方程模型来估计胸腺细胞总量及各种未成熟或成熟细胞所占的比例.本文在利用准静态近似法的基础之上,采用微分方程稳定性理论中的有关方法对这类微分方程模型的稳定性等问题进行了完整的理论分析,所获得的其平衡位置为全局渐近稳定的结论为有关文献中采用数值模拟所预测的结论的正确性提供了理论依据.

Stability Analysis on a Nonlinear Model of T Cell Development in the Thymus

T cells begin their development as precursor cells in the bone marrow.These cells migrate to the thymus,where they further divide,differentiate and mature into functional T cells.In ,the authors developed a differential equation model to describe cell proliferation,differentiation and death in the thymus that can account for both the total number of thymus cells and fractions of various types of immature and mature thymocytes.This model was designed to analyze the differentiation of thymocytes and thymic selection.In this paper,based on the methods of quasi-steady-state approximation and Liapunov functions,we give a completely theoretical analysis on the existence of the nonnegative solutions and the local and global asymptotic stability of the positive equilibria of the model.Furthermore,we also give some numerical simulations to support our theoretical results.