论文标题
造血干细胞动力学非自主数学模型的周期性解决方案
Periodic solutions for a nonautonomous mathematical model of hematopoietic stem cell dynamics
论文作者
论文摘要
本文的主要目的是研究非自主差分差异系统的周期性解决方案，该系统描述了在细胞周期水平的某些外部周期性调节因素下，描述了造血干细胞（HSC）种群的动力学。起始模型是一个非自主系统，该系统由两个年龄结构化的偏微分方程，描述了静态（$ g_0 $）和增殖（$ g_1 $，$ s $，$ s $，$ g_2 $和$ m $）阶段。我们对定期时间变化的系数的影响感兴趣，例如昼夜节律或某些药物的周期性使用对HSC种群的动力学的影响。特征的方法将年龄结构化模型降低为非自主差分差异系统。我们使用拓扑学度技术和固定点方法（我们模型的周期性解决方案的存在）在适当的条件下在适当的条件下证明了系统的参数。
The main purpose of this paper is to study the existence of periodic solutions for a nonautonomous differential-difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory factors at the cellular cycle level. The starting model is a nonautonomous system of two age-structured partial differential equations describing the HSC population in quiescent ($G_0$) and proliferating ($G_1$, $S$, $G_2$ and $M$) phase. We are interested on the effects of a periodically time varying coefficients due for example to circadian rhythms or to the periodic use of certain drugs, on the dynamics of HSC population. The method of characteristics reduces the age-structured model to a nonautonomous differential-difference system. We prove under appropriate conditions on the parameters of the system, using topological degree techniques and fixed point methods, the existence of periodic solutions of our model.
