On a mathematical model for cancer invasion with repellent pH-taxis and nonlocal intraspecific interaction

TL;DR

This paper develops a mathematical model for cancer invasion that incorporates pH-taxis and nonlocal cell interactions, providing analytical results and numerical simulations to understand pattern formation.

Contribution

It introduces a reaction-diffusion-taxis model with nonlocal interactions and proves key properties like existence and uniqueness of solutions.

Findings

Global existence and uniqueness of solutions

Pattern formation in 1D simulations

Numerical illustrations of solution behavior

Abstract

Starting from a mesoscopic description of cell migration and intraspecific interactions we obtain by upscaling an effective reaction-difusion-taxis equation for the cell population density involving spatial nonlocalities in the source term and biasing its motility and growth behavior according to environmental acidity. We prove global existence, uniqueness, and boundedness of a nonnegative solution to a simplified version of the coupled system describing cell and acidity dynamics. A 1D study of pattern formation is performed. Numerical simulations illustrate the qualitative behavior of solutions.