Global classical solutions for a metastatic cancer invasion model with negative haptotaxis

Abstract

We analyze a coupled PDE-ODE model for metastatic cancer invasion involving epithelial-like and mesenchymal-like cancer cells, cancer-associated fibroblasts (CAFs), the transforming growth factor $β$, matrix-degrading metalloproteinases, and extracellular matrix reconstruction by CAFs. The model incorporates bidirectional phenotypic transitions between epithelial-like and mesenchymal-like cancer cells, cancer-cell haptotaxis, negative fibroblast haptotaxis, as well as cell-specific proliferation. Under explicit parameter restrictions, we establish global classical solvability for the full model in two dimensions using an energy-based approach, and for a three-dimensional variant with constant phenotypic transition rates using coupled $L^p$-estimates. Numerical simulations illustrate primary tumor invasion and metastatic spread to secondary sites.