Stem and precursor cells play a critical role in tissue development, maintenance, and repair throughout the life. Often, experimental limitations prevent direct observation of the stem cell compartment, thereby posing substantial challenges to the analysis of such cellular systems. Two-type age-dependent branching processes with immigration are proposed to model populations of progenitor cells and their differentiated progenies. Immigration of cells into the pool of progenitor cells is formulated as a non-homogeneous Poisson process. The asymptotic behavior of the process is governed by the largest of two Malthusian parameters associated with embedded Bellman-Harris processes. Asymptotic approximations to the expectations of the total cell counts are improved by Markov compensators.

中文翻译：

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由具有非均质迁移的两种可减少年龄相关分支过程描述的细胞群的渐近行为

干细胞和前体细胞在整个生命过程中的组织发育、维护和修复中发挥着关键作用。通常，实验限制阻止直接观察干细胞区室，从而对此类细胞系统的分析构成重大挑战。提出了两种类型的具有迁移的年龄依赖性分支过程来模拟祖细胞群及其分化的后代。细胞向祖细胞池的迁移被制定为非均质泊松过程。该过程的渐近行为受与嵌入的 Bellman-Harris 过程相关的两个马尔萨斯参数中最大的一个控制。马尔可夫补偿器改进了对总细胞计数期望的渐近近似。