A strongly degenerate diffusion‐haptotaxis model of tumour invasion under the go‐or‐grow dichotomy hypothesis

Abstract

We propose and study a strongly coupled PDE‐ODE‐ODE system modeling cancer cell invasion through a tissue network under the go‐or‐grow hypothesis asserting that cancer cells can either move or proliferate. Hence, our setting features 2 interacting cell populations with their mutual transitions and involves tissue‐dependent degenerate diffusion and haptotaxis for the moving subpopulation. The proliferating cells and the tissue evolution are characterized by way of ODEs for the respective densities. We prove the global existence of weak solutions and illustrate the model behaviour by numerical simulations in a 2‐dimensional setting. The numerical results recover qualitatively the infiltrative patterns observed histologically and moreover allow to establish a qualitative relationship between the structure of the tissue and the expansion of the tumour, thereby paying heed to its heterogeneity.