相关论文: Invasion fronts and adaptive dynamics in a model f…
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However,…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This…
Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…
In this paper we analyse a previously proposed cell-based model of glioblastoma (brain tumour) growth, which is based on the assumption that the cancer cells switch phenotypes between a proliferative and motile state (Gerlee and Nelander,…
We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type…
The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migration of cell populations driven by this non-local form of…
Chemotaxis-driven invasions have been proposed across a broad spectrum of biological processes, from cancer to ecology. The influential system of equations introduced by Keller and Segel has proven a popular choice in the modelling of such…
In this paper we study a reduced continuous model describing the local evolution of high grade gliomas - a lethal type of primary brain tumor - through the interplay of different cellular phenotypes. We show how hypoxic events, even…
The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
We consider a population structured by a spacevariable and a phenotypical trait, submitted to dispersion,mutations, growth and nonlocal competition. This population is facing an {\it environmental gradient}: to survive at location $x$, an…
Cell invasion and spatial pattern formation are two distinct manifestations of cellular self-organisation in development, regeneration, and disease. Here, we develop and analyse a unified theoretical framework that links these two seemingly…
We consider a multiscale stochastic compartmental model with three types of cells (stem cells, immature cells and mature cells) which combines cell proliferation and cell differentiation. We derive a hydrodynamic limit when the number of…
A fundamental feature of collective cell migration is phenotypic heterogeneity which, for example, influences tumour progression and relapse. While current mathematical models often consider discrete phenotypic structuring of the cell…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into account anisotropic cell movement and oxygen diffusion…