Stability of a mathematical model of tumour-induced angiogenesis
Articles
Dan Li
University of Science and Technology, China
Wanbiao Ma
University of Science and Technology, China
Songbai Guo
University of Science and Technology, China
Published 2016-05-20
https://doi.org/10.15388/NA.2016.3.3
PDF

Keywords

cancer
angiogenic factors
time delay
stability

How to Cite

Li, D., Ma, W. and Guo, S. (2016) “Stability of a mathematical model of tumour-induced angiogenesis”, Nonlinear Analysis: Modelling and Control, 21(3), pp. 325–344. doi:10.15388/NA.2016.3.3.

Abstract

A model consisting of three differential equations to simulate the interactions between cancer cells, the angiogenic factors and endothelial progenitor cells in tumor growth is developed. Firstly, the global existence, nonnegativity and boundedness of the solutions are discussed. Secondly, by analyzing the corresponding characteristic equations, the local stability of three boundary equilibria and the angiogenesis equilibrium of the model is discussed, respectively. We further consider global asymptotic stability of the boundary equilibria and the angiogenesis equilibrium by using the well-known Liapunov–LaSalle invariance principal. Finally, some numerical simulations are given to support the theoretical results.

PDF

Downloads

Download data is not yet available.