Open AccessStability of a mathematical model of tumour-induced angiogenesis
Author(s) -
Dan Li,
Wanbiao Ma,
Shuaiqi Guo
Publication year - 2016
Publication title -
nonlinear analysis
Language(s) - English
Resource type - Journals
eISSN - 2335-8963
pISSN - 1392-5113
DOI - 10.15388/na.2016.3.3
Subject(s) - angiogenesis , boundary (topology) , stability (learning theory) , mathematics , exponential stability , differential equation , boundary value problem , mathematical analysis , physics , computer science , nonlinear system , cancer research , medicine , quantum mechanics , machine learning
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.