Related papers: Micro-Macro Derivation of Virus-Chemotaxis Models
This paper deals with the micro-macro derivation of models from the underlying description provided by methods of the kinetic theory for active particles. We consider the so-called exotic models according to the definition proposed in in…
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are…
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or…
We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…
This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a…
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…
We compare chemotaxis, the migration of cells and higher animals in reaction to a chemical stimulus, and similar phenomena originating within gases from temperature differences. Then we explain two easy mathematical models for handling…
Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and…
We discuss velocity-jump models for chemotaxis of bacteria with an internal state that allows the velocity jump rate to depend on the memory of the chemoattractant concentration along their path of motion. Using probabilistic techniques, we…
Chemotaxis is a directed cell movement in response to external chemical stimuli. In this paper, we propose a simple model for the origin of chemotaxis - namely how a directed movement in response to an external chemical signal may occur…
Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulations with additional terms accounting for spatial dynamics,…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
In this paper we consider a biased velocity jump process with excluded-volume interactions for chemotaxis, where we account for the size of each particle. Starting with a system of N individual hard rod particles in one dimension, we derive…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
The mathematical formulation of the model for molecular movement of single motor proteins driven by cyclic biochemical reactions in an aqueous environment leads to a drifted Brownian motion characterized by coupled diffusion equations. In…