Analysis of a Nonlinear Age-Structured Model for Tumor Cell Populations with Quiescence


主讲人:陈静 诺瓦东南大学博士




主讲人介绍:陈静,2015年从美国迈阿密大学(University of  Miami)数学系获得应用数学博士学位,毕业后留校从事博士后研究,至2018年8月起在位于美国佛罗里达州劳德代尔堡市的诺瓦东南大学数学系工作至今。主要研究方向是微分方程、动力系统、数学传染病学和种群生物学等,在SIAM  J Appl Math、PLoS Neg Trop Dis、J Theor Biol、J Nonlinear Sci、Bull Math Biol、J Dyn  Differ Equ等权威学术期刊发表论文10多篇。

内容介绍:We present a nonlinear first-order hyperbolic partial differential equation  model to describe age-structured tumor cell populations with proliferating and  quiescent phases at the avascular stage in vitro. The division rate of the  proliferating cells is assumed to be nonlinear due to the limitation of the  nutrient and space. The model includes a proportion of newborn cells that enter  directly the quiescent phase with age zero. This proportion can reflect the  effect of treatment by drugs such as erlotinib. The existence and uniqueness of  solutions are established. The local and global stabilities of the trivial  steady state are investigated. The existence and local stability of the positive  steady state are also analyzed. Numerical simulations are performed to verify  the results and to examine the impacts of parameters on the nonlinear dynamics  of the model.