Open AccessNonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion
Author(s) -
Youshan Tao,
J. Ignacio Tello
Publication year - 2016
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2016.13.193
Subject(s) - clearance , ode , tumor microenvironment , tumor cells , diffusion , competition (biology) , logistic function , tumor progression , biology , reaction–diffusion system , microbiology and biotechnology , chemistry , biological system , biophysics , cancer research , mathematics , medicine , cancer , physics , ecology , genetics , thermodynamics , mathematical analysis , statistics , urology
This work studies a general reaction-diffusion model for acid-mediated tumor invasion, where tumor cells produce excess acid that primarily kills healthy cells, and thereby invade the microenvironment. The acid diffuses and could be cleared by vasculature, and the healthy and tumor cells are viewed as two species following logistic growth with mutual competition. A key feature of this model is the density-limited diffusion for tumor cells, reflecting that a healthy tissue will spatially constrain a tumor unless shrunk. Under appropriate assumptions on model parameters and on initial data, it is shown that the unique heterogeneous state is nonlinearly stable, which implies a long-term coexistence of the healthy and tumor cells in certain parameter space. Our theoretical result suggests that acidity may play a significant role in heterogeneous tumor progression.