We briefly review spatially homogeneous mechanistic mathematical models describing the
interactions between a malignant tumor and the immune system. We begin with the simplest …

Cancer is a complex and heterogeneous disease that exhibits high levels of robustness
against various therapeutic interventions. It is a constellation of diverse and evolving …

The mortality of patients with solid tumors is mostly due to metastasis that relies on the
interplay between migration and proliferation. The “go or grow” hypothesis postulates that …

TGF-β is an immunoregulatory protein that contributes to inadequate antitumor immune
responses in cancer patients. Recent experimental data suggests that TGF-β inhibition …

We provide a tool for data-driven modeling of motility, data being time-lapse recorded
trajectories. Several mathematical properties of a model to be found can be gleaned from …

We present a mathematical study of the emergence of phenotypic heterogeneity in
vascularized tumors. Our study is based on formal asymptotic analysis and numerical …

We consider a model for the dynamics of growing cell populations with heterogeneous
mobility and proliferation rate. The cell phenotypic state is described by a continuous …

In this paper, we develop a non-local mathematical model describing cancer cell invasion
and movement as a result of integrin-controlled cell–cell adhesion and cell–matrix adhesion …

Background We study the selection dynamics in a heterogeneous spatial colony of cells. We
use two spatial generalizations of the Moran process, which include cell divisions, death and …

This article analyzes the mathematical model which is described by the nonlinear partial
differential equation governing the density of cancer cells at any position (x, y) in the open …