Ackleh Azmy S, Deng Keng, Ito Kazufumi, Thibodeaux Jeremy
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, USA.
Math Biosci. 2006 Nov;204(1):21-48. doi: 10.1016/j.mbs.2006.08.004. Epub 2006 Aug 18.
We develop a quasilinear structured model that describes the regulation of erythropoiesis, the process in which red blood cells are developed. In our model, the maturation velocity of precursor cells is assumed to be a function of the erythropoietin hormone, and the decay rate of this hormone is assumed to be a function of the number of precursor cells, unlike other models which assume these parameters to be constants. Existence-uniqueness results are established and convergence of a finite difference approximation to the unique solution of the model is obtained. The finite difference scheme is then used to investigate the effects of these nonlinear parameters on the model dynamics. Our results show that a velocity of precursor cells maturation rate which is an increasing function of the hormone level and a decay rate of the hormone which is an increasing function of the number of precursor cells have a stabilizing effect on the dynamics of the model. While assuming that one parameter is a function and letting the other be a constant stabilizes the oscillations in the mature cells level, the effect is more significant when both parameters are taken to be functions. A study of robustness with respect to the forms of these functions and parameter sensitivity is also carried out.
我们构建了一个拟线性结构模型，该模型描述了红细胞生成（即红细胞发育过程）的调节机制。在我们的模型中，前体细胞的成熟速度被假定为促红细胞生成素的函数，并且该激素的衰减率被假定为前体细胞数量的函数，这与其他将这些参数假定为常数的模型不同。我们建立了存在唯一性结果，并获得了有限差分近似对模型唯一解的收敛性。然后使用有限差分格式来研究这些非线性参数对模型动态的影响。我们的结果表明，前体细胞成熟率速度是激素水平的增函数，且激素衰减率是前体细胞数量的增函数，这对模型动态具有稳定作用。虽然假定一个参数为函数而另一个为常数会使成熟细胞水平的振荡稳定，但当两个参数都被视为函数时，这种效果更为显著。我们还对这些函数形式的稳健性和参数敏感性进行了研究。
