A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy.
A time-delayed mathematical model for tumor growth with the effect of periodic therapy is studied. The establishment of the model is based on the reaction-diffusion dynamics and mass conservation law and is considered with a time delay in cell proliferation process. Sufficient conditions for the global stability of tumor free equilibrium are given. We also prove that if external concentration of nutrients is large the tumor will not disappear and the conditions under which there exist periodic solutions to the model are also determined. Results are illustrated by computer simulations.
School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong 526061, China.
Shihe
S
Xu
Teaching Research Administration of Guangrao County, Dongying, Shandong 257300, China.
Xiangqing
X
Wei
College of Transport and Communications, Shanghai Maritime University, Shanghai 201306, China.
Fangwei
F
Zhang
D000465:Algorithms; D017209:Apoptosis; D049109:Cell Proliferation; D003198:Computer Simulation; D004058:Diffusion; D006801:Humans; D008962:Models, Theoretical; D009369:Neoplasms / Q000503:physiopathology* / Q000628:therapy*; D013997:Time Factors; D016896:Treatment Outcome