Dynamics and numerical simulations in a production and development of red blood cells with one delay
Dynamics and numerical simulations in a production and development of red blood cells with one delay
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DOI：
10.1016/j.cnsns.2007.08.012
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发表时间：
2008-08
期刊：
影响因子：
--
通讯作者：
R. Yafia
中科院分区：
文献类型：
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作者：
R. Yafia
在本文中，我们研究了Grabosch和Heijmans [Grabosch A，Heijmans HJAM.红细胞的产生、发育和成熟，一个数学模型。AM-R 8919，ISSN 0924-2953，1989年。]模型细胞群体是由一个系统的微分方程与一个延迟。基本假设是负责产生血细胞的细胞群由三个部分组成：干细胞，前体细胞和血细胞。我们证明了该模型有两个可能的稳定状态和他们的动态（取决于时间延迟）的局部稳定性方面进行了研究，我们说明了这些结果与数值模拟的一些不同的时间延迟值。
In this paper, we study an unstructured model of a cellular population in the spirit of Grabosch and Heijmans [Grabosch A, Heijmans HJAM. Production, development and maturation of red blood cells, A mathematical model. AM-R 8919, ISSN 0924-2953, 1989.] model. The cellular population is described by a system of differential equations with one delay. The basic assumption is that the cell population responsible for the production of blood cells consists of three compartments: the stem cells, the precursor cells, and the blood cells. We prove that the model has two possible steady states and their dynamics (depending on time delay) are studied in term of the local stability, we illustrate these results with numerical simulations for some different values of the time delay.