Related papers: A reaction-diffusion model for relapsing-remitting…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
We introduce a spatially extended mathematical model for Duchenne muscular dystrophy based on a damage-driven paradigm, in which immune recruitment is triggered by tissue injury. The model is formulated as a reaction--diffusion--chemotaxis…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns…
We consider a multi-species reaction-diffusion system that arises in epidemiology to describe the spread of several strains, or variants, of a disease in a population. Our model is a natural spatial, multi-species, extension of the…
This paper aims to investigate a reaction-diffusion model which describes in-host infection for Mycobacterium tuberculosis (Mtb) allowing random motion (i.e. linear diffusion) and chemotaxis (i.e. non-linear diffusion) of macrophages and…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
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…
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 immune responses. We develop two kinetic models: one describes a…
Mathematical and computational modelling in oncology has played an increasingly important role in not only understanding the impact of various approaches to treatment on tumour growth, but in optimizing dosing regimens and aiding the…
We investigated existence of global weak solutions for a system of chemotaxis type with nonlinear degenerate diffusion, arising in modelling Multiple Sclerosis disease. The model consists of three equations describing the evolution of…
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
Currently, free flaps and pedicled flaps are assessed for reperfusion in post-operative care using colour, capillary refill, temperature, texture and Doppler signal (if available). While these techniques are effective, they are prone to…
In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human…
The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share…