Related papers: A stochastic model for wound healing
The paper presents a computational stochastic model of virtual cells irradiation, based on Quasi-Markov Chain Monte Carlo method and using biophysical input. The model is based on a stochastic tree of probabilities for each cell of the…
The steady state properties of the mean density population of infected cells in a viral spread is simulated by a general forest fire like cellular automaton model with two distinct populations of cells ( permissive and resistant ones) and…
We present an novel framework for efficiently and effectively extending the powerful continuous diffusion processes to discrete modeling. Previous approaches have suffered from the discrepancy between discrete data and continuous modeling.…
The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…
We use a simple, collision-based, discrete, random abrasion model to compute the profiles for the stoss faces in a bedrock abrasion process. The model is the discrete equivalent of the generalized version of a classical, collision based…
We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context…
Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe,…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…
Wounds in epithelial tissues compromise their vital role in homeostasis. A rapid and efficient wound healing encompasses different mechanisms, which includes the formation of a contractile actin-myosin cable around its edge, known as the…
Tumor-immune interactions are central to cancer progression and treatment outcomes. In this study, we present a stochastic agent-based model that integrates cellular heterogeneity, spatial cell-cell interactions, and drug resistance…
We deal with a small enough tumor section to consider it homogeneous, such that populations of lymphocytes and cancer cells are independent of spatial coordinates. A stochastic model based in one step processes is developed to take into…
In this paper, we carry out a travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion. We consider two types of invasive fronts of tumour tissue into extracellular matrix (ECM), which represents…
The use of oncolytic viruses as cancer treatment has received considerable attention in recent years, however the spatial dynamics of this viral infection is still poorly understood. We present here a stochastic agent-based model describing…
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…
In this paper, we derive a new chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migration process for its early and late stages. Different from the…
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…
As a concrete setting where stochastic partial differential equations (SPDEs) are able to model real phenomena, we propose a stochastic Meinhardt model for cell repolarisation and study how parameter estimation techniques developed for…
We study extended infection fronts advancing over a spatially uniform susceptible population by solving numerically a diffusive Kermack McKendrick SIR model with a dichotomous spatially random transmission rate, in two dimensions. We find a…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…