We propose a minimal mathematical framework to describe the go-or-grow dynamics of tumor cells comprising two phenotypically distinct populations. One population is migratory and undergoes linear diffusion, while the other proliferates in an oxygen-dependent manner. The local oxygen concentration governs transitions between these phenotypes. We then ask whether these two coupled phenotype-specific equations can be reduced to a single mixed-phenotype equation under cyclic hypoxia. We establish a connection between the minimal go-or-grow model with distinct phenotypic populations and a reduced model describing a single-cell population with oxygen-dependent diffusion and proliferation in the fast-phenotypic-switching regime. This theoretical reduction is validated through numerical simulations.
@article{arxiv.2602.23042,
title = {A Single Equation Explains Go-or-Grow Dynamics in Cyclic Hypoxia},
author = {Gopinath Sadhu and Philip K Maini and Mohit Kumar Jolly},
journal= {arXiv preprint arXiv:2602.23042},
year = {2026}
}