In this paper, we focus on numerical approximations of Piecewise Diffusion Markov
Processes (PDifMPs), particularly when the explicit flow maps are unavailable. Our …

We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells,
macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno …

Starting from kinetic transport equations and subcellular dynamics we deduce a multiscale
model for glioma invasion relying on the go-or-grow dichotomy and the influence of …

A multiscale model for glioma spread in brain tissue under the influence of vascularization
and vascular endothelial growth factors is proposed. It accounts for the interplay between …

We deduce a model for glioma invasion that accounts for the dynamics of brain tissue being
actively degraded by tumor cells via excessive acidity production, but also according to the …

We propose a mathematical kinetic framework to investigate interactions between tumor
cells and the immune system, focusing on the spatial dynamics of tumor progression and …

Cells perform directed motion in response to external stimuli that they detect by sensing the
environment with their membrane protrusions. Precisely, several biochemical and …

Glioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been
numerous attempts to model the invasion of tumorous glioma cells via partial differential …

Go-or-grow approaches represent a specific class of mathematical models used to describe
populations where individuals either migrate or reproduce, but not both simultaneously …

Tumor cell migration within the microenvironment is a crucial aspect for cancer progression
and, in this context, hypoxia has a significant role. An inadequate oxygen supply acts as an …