细胞老化和生长速率的变化如何影响马尔萨斯参数？
How does variability in cells aging and growth rates influence the malthus parameter?
摘要：
本研究的目的是通过马尔萨斯参数来比较不同细胞群的生长速度。我们关注年龄结构和尺寸结构方程。第一群体（参照）由全部以相同速率老化或生长的细胞组成，所述速率为$\bar v$。第二群体（具有可变性）由细胞组成，每个细胞以根据具有平均值$\bar v$的非退化分布$ρ$绘制的速率$v$老化或生长。在第一部分中，分析答案-基于特征问题的研究-提供了年龄结构模型。在第二部分中，数值答案-基于随机模拟-推导出的大小结构模型。从数值上看，具有变异性的群体比参考群体增殖得更慢（对于实验上合理的分裂率）。我们测量的Malthus参数的减少，对于实际变异系数约为15-20\%的分布$ρ$约为2%，是决定性的，因为它控制着整个种群的{ \it指数}增长。
英文摘要：
The aim of this study is to compare the growth speed of different cell populations measured by their Malthus parameter. We focus on both the age-structured and size-structured equations. A first population (of reference) is composed of cells all aging or growing at the same rate $\bar v$. A second population (with variability) is composed of cells each aging or growing at a rate $v$ drawn according to a non-degenerated distribution $ρ$ with mean $\bar v$. In a first part, analytical answers -- based on the study of an eigenproblem -- are provided for the age-structured model. In a second part, numerical answers -- based on stochastic simulations -- are derived for the size-structured model. It appears numerically that the population with variability proliferates more slowly than the population of reference (for experimentally plausible division rates). The decrease in the Malthus parameter we measure, around 2% for distributions $ρ$ with realistic coefficients of variations around 15-20\%, is determinant since it controls the {\it exponential} growth of the whole population.
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