Related papers: A stochastic model for wound healing
For the regime-switching diffusion process with and without advection term we propose an integro-differential equation describing the densities of states continuously distributed over a segment. We demonstrate that there exists a…
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…
In this paper, we shall establish the spreading speed and existence of traveling waves for a non-cooperative system arising from epidermal wound healing and characterize the spreading speed as the slowest speed of a family of non-constant…
We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
Adoptive Cell Transfer therapy of cancer is currently in full development and mathematical modeling is playing a critical role in this area. We study a stochastic model developed by Baar et al. in 2015 for modeling immunotherapy against…
We investigate numerically and theoretically the precursory intermittent activity characterizing the preliminary phase of damage accumulation prior to failure of quasi-brittle solids. We use a minimal but thermodynamically consistent model…
In this study, we model avascular tumour growth in epithelial tissue. This can help us to get a macroscopic view of the interaction between the tumour with its surrounding microenvironment and the physical changes within the tumour…
The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory. As there is a clear corresponding stochastic process,…
Wound geometry and the mechanical properties of human skin govern the failure modes of partially healed or scarred tissue. Though dermatologists and surgeons develop an intuitive understanding of the mechanical characteristics of skin…
Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely…
Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we…
A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using piecewise diffusion Markov processes (PDifMPs) at the cellular level, we derive an equation for the…
This paper theoretically analyzes a phenomenological stochastic model for bacterial growth. This model comprises cell division and the linear growth of cells, where growth rates and cell cycles are drawn from lognormal distributions. We…
We present two approaches to study invasion in growth-fragmentation-death mod- els. The first one is based on a stochastic individual based model, which is a piecewise deterministic branching process with a continuum of types, and the…
We consider a stochastic model, describing the growth of two competing infections on $\mathbb{R}^d$. The growth takes place by way of spherical outbursts in the infected region, an outburst in the type 1 (2) infected region causing all…
100 years after Smoluchowski introduces his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from large…
A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exhibits velocity locking, where rational speed invasion fronts…
These notes describe stochastic epidemics in a homogenous community. Our main concern is stochastic compartmental models (i.e. models where each individual belongs to a compartment, which stands for its status regarding the epidemic under…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…