Mathematics Faculty Articles

Title

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

Document Type

Article

Publication Date

10-2018

Publication Title

Journal of Nonlinear Science

Keywords

Cell cycle, Age-structured model, Proliferating and quiescent stages, Steady state, Stability

ISSN

0938-8974

Volume

28

Issue/No.

5

First Page

1763

Last Page

1791

Abstract

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.

Comments

©Springer Science+Business Media, LLC, part of Springer Nature 2018

Additional Comments

National Natural Science Foundation of China grant #s: 11401060, 11401117, 11401217, 11771168; Basic and Advanced Research Project of Chonqing grant #: cstc2016jcyjA0412; Program of Chongqing Innovation Team Project #: CXTDX201601022; Chonqing Municipal Education Commission grant #s: KJ1600522, KJ1705136

DOI

10.1007/s00332-018-9463-0

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