Related papers: A reaction-diffusion model for Mycobacterium tuber…
We study the coupled two-species non-equilibrium reaction-controlled diffusion model introduced by Trimper et al. [Phys. Rev. E 62, 6071 (2000)] by means of detailed Monte Carlo simulations in one and two dimensions. Particles of type A may…
The formation of self-organized patterns is key to the morphogenesis of multicellular organisms, although a comprehensive theory of biological pattern formation is still lacking. Here, we propose a minimal model combining tissue mechanics…
This work deals with a parabolic chemotaxis model with nonlinear diffusion and nonlocal reaction source. The problem is formulated on the whole space and, depending on a specific interplay between the coefficients associated to such…
Tuberculosis is one of the most lethal contagious diseases caused by Mycobacterium tuberculosis (MTB), in many cases, the infected did not show any symptoms, because the bacilli entered the dormant stage in granulomas. The dormant stage of…
Chemotaxis in bacteria such as \textit{E.\ coli} is controlled by the slow methylation of chemoreceptors. As a consequence, intrinsic time and length scales of tens of seconds and hundreds of micrometers emerge, making the Keller--Segel…
Motivated by recent outbreaks of the Ebola Virus, we are concerned with the role that a vector reservoir plays in supporting the spatio-temporal spread of a highly lethal disease through a host population. In our context, the reservoir is a…
Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive.…
In this article a kinetic model for the dynamics of myxobacteria colonies on flat surfaces is investigated. The model is based on the kinetic equation for collective bacteria dynamics introduced in arXiv:2001.02711, which is based on the…
This paper is framed in a series of studies on attraction-repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities and logistic sources, for the dynamics of the cell density, and consumption and/or…
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 show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…
Enzymes show two distinct transport behaviors in the presence of their substrates in solution. First, their diffusivity enhances with increasing substrate concentration. In addition, enzymes perform directional motion toward regions with…
Chemotaxis is the physical phenomenon that bacteria adjust their motions according to chemical stimulus. A classical model for this phenomenon is a kinetic equation that describes the velocity jump process whose tumbling/transition kernel…
In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous distribution of vasculature. Together with different nutrient…
Bacterial cells navigate around their environment by directing their movement along chemical gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial populations into previously unoccupied territories.…
Micro-organisms aggregate through chemotaxis against a concentration gradient of signals secreted by themselves. We have numerically studied a model consisting of elements with intracellular dynamics, random walks with a state-dependent…
The goal of this work is to understand and quantify how a line with nonlocal diffusion given by an integral enhances a reaction-diffusion process occurring in the surrounding plane. This is part of a long term programme where we aim at…
Mathematical models have been widely used to describe the collective movement of bacteria by chemotaxis. In particular, bacterial concentration waves traveling in a narrow channel have been experimentally observed and can be precisely…
Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…