Analysis of a mathematical model for tumor growth under indirect effect of inhibitors with time delay in proliferation

被引：18

作者：

Xu, Shihe ^{[2
]}

Feng, Zhaoyong ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

[2] Zhaoqing Univ, Dept Math, Zhaoqing 526061, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 374卷 / 01期

关键词：

Tumor growth; Inhibitors; Time delay; Local stability; Global stability; INTERNALIZATION; ABSENCE; CELLS;

D O I：

10.1016/j.jmaa.2010.08.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a mathematical model for tumor growth with time delay in proliferation under indirect effect of inhibitor is studied. The delay represents the time taken for cells to undergo mitosis. Nonnegativity of solutions is investigated. The steady-state analysis is presented with respect to the magnitude of the delay. Existence of Hopf bifurcation is proved for some parameter values. Local and global stability of the stationary solutions are proved for other ones. The analysis of the effect of inhibitor's parameters on tumor's growth is presented. The results show that dynamical behavior of solutions of this model is similar to that of solutions for corresponding non-retarded problems for some parameter values. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.

引用

页码：178 / 186

页数：9

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