On a PDE-ODE-PDE model for two interacting cell populations under the influence of an acidic environment and with nonlocal intra- and interspecific growth limitation

TL;DR

This paper introduces a coupled PDE-ODE model describing two interacting cell populations influenced by acidity, incorporating nonlocal growth limitations and phenotype transitions, with proven global existence and numerical exploration of pattern formation.

Contribution

It develops a novel PDE-ODE-PDE framework for cell interactions under acidity, proving global solutions and analyzing patterning through simulations.

Findings

Global existence of weak solutions established.

Numerical simulations reveal conditions for pattern formation.

Model captures phenotype switching influenced by acidity.

Abstract

We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or decay, according to the strength of spatially nonlocal intra- and interspecific interactions. The two cell phenotypes are interchangeable, the transitions depending on the environmental acidity. We prove global existence of a weak solution to the considered PDE-ODE-PDE system and perform numerical simulations in 1D to informally investigate boundedness and patterning behavior in dependence of the system's parameters and kernels involved in the nonlocal terms.