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

被引：0
作者：
Zijian Liu
Jing Chen
Jianhua Pang
Ping Bi
Shigui Ruan
机构：
[1] Chongqing Jiaotong University,College of Mathematics and Statistics
[2] University of Miami,Department of Mathematics
[3] Guangxi University of Science and Technology,School of Science
[4] East China Normal University,Department of Mathematics, Shanghai Key Laboratory of PMMP
[5] University of Miami Miller School of Medicine,Sylvester Comprehensive Cancer Center
来源：
Journal of Nonlinear Science | 2018年 / 28卷
关键词：
Cell cycle; Age-structured model; Proliferating and quiescent stages; Steady state; Stability; 35L40; 35B35; 92C37;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：1763 / 1791
页数：28
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