Analysis of a time-delayed mathematical model for tumour growth with inhibitors

Abstract

In this article, we study the fully non-stationary version of a mathematical model for tumour growth under indirect effect of inhibitor with time delay in proliferation. The quasi-stationary version has been studied by our previous work [S. Xu and Z. Feng, Analysis of a mathematical model for tumour growth under indirect effect of inhibitors with time delay in proliferation, J. Math. Anal. Appl. 374 (2011), pp. 178–186]. The existence and uniqueness of a global solution are proved and the asymptotic behaviour of the solution is studied. The results show that the dynamical behaviour of solutions of the fully non-stationary and the quasi-stationary version are similar under some conditions.

Keywords:

• tumour growth
• inhibitors
• time delay
• global solution
• asymptotic behaviour

AMS Subject Classifications::

• 34K12
• 35B35
• 35K57

Acknowledgements

The authors express their thanks to two anonymous references for their valuable suggestions on modification of the original manuscript. S. Xu and M. Bai are partially supported by NSF of China (11171295), NSF and YMF of Guangdong Province of China (S2011040001407, LYM10133). X. Zhao is partially supported by NSF of Zhejiang Province of China (Y6110074).