Global Stability of a PDE-ODE model for acid-mediated tumor invasion

TL;DR

This paper analyzes the global behavior of a reaction-diffusion PDE-ODE model for acid-mediated tumor invasion, revealing how acid resistance and cell competition influence long-term tumor dynamics.

Contribution

It introduces a novel PDE-ODE model with density-limited diffusion and provides theoretical analysis of tumor progression using Lyapunov functionals.

Findings

Conditions for coexistence or dominance of tumor cells.

Impact of acid resistance on tumor invasion outcomes.

Mathematical characterization of long-term tumor dynamics.

Abstract

In this paper, we study the global dynamics of a general reaction-diffusion model based on acid-mediated invasion hypothesis, which is a candidate explanation for the Warburg effect. A key feature of this model is the density-limited tumor diffusion term for tumor cells, which might give rise to the degeneracy of the parabolic equation. Our theoretical results characterize the effects of acid resistance and mutual competition of healthy cells and tumor cells on tumor progression in the long term, i.e., whether the healthy cells and tumor cells coexist or the tumor cells prevail after tumor invasion. The approach relies on the construction of suitable Lyapunov functionals and upper/lower solutions.