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The purpose of this work is the study of \textit{chemotaxis} and how to model it through the equations of Keller-Segel. \textit{Chemotaxis} is a natural process which induces the organisms to direct their movement according to certain…
Chemotaxis is typically modeled in the context of cellular motion towards a static, exogenous source of chemoattractant. Here, we propose a time-dependent mechanism of chemotaxis in which a self-propelled particle ({\it e.g.}, a cell)…
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…
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions; one example is the immune system signalling, where infected tissues release chemokines…
Chemotaxis refers to the directed movement of cells in response to a chemical signal called chemoattractant. A crucial point in the mathematical modeling of chemotactic processes is the correct description of the chemotactic sensitivity and…
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions. One example is the immune system signalling, where infected tissues release chemokines…
Chemotaxis, the directional locomotion of cells towards a source of a chemical gradient, is an integral part of many biological processes - for example, bacteria motion, single-cell or multicellular organisms development, immune response,…
Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller-Segel equation and a…
A simple model is studied for the chemotactic movement of biological cells in the presence of a periodic chemical wave. It incorporates the feature of adaptation that may play an important role in allowing for ``rectified" chemotaxis:…
This paper studies a chemotaxis system where cells move in response to a chemical signal within a confined habitat. The model includes external source terms that combine local and nonlocal growth with dampening effects. The main focus is on…
Chemotaxis combines three processes: directional sensing, polarity reorientation and migration. Directed migration plays an important role in immune response, metastasis, wound healing and development. To describe chemotaxis, we extend a…
Chemotaxis is the process by which cells behave in a way that follows the chemical gradient. Applications to bacteria growth, tissue inflammation, and vascular tumors provide a focus on optimization strategies. Experiments can characterize…
Chemotaxis is a fundamental mechanism of cells and organisms, which is responsible for attracting microbes to food, embryonic cells into developing tissues, or immune cells to infection sites. Mathematically chemotaxis is described by the…
A stochastic walker model is proposed to describe the chemotactic guidance of growth cones, i.e. the tips of developing neurites. The model accounts for the influence of both attractive and repulsive chemical cues, which are emitted by the…
Motivated by observations of the dynamics of {\it Myxococcus xanthus}, we present a self-interacting random walk model that describes the competition between chemokinesis and chemotaxis. Cells are constrained to move in one dimension, but…
Aerotaxis is the particular form of chemotaxis in which oxygen plays the role of both the attractant and the repellent. Aerotaxis occurs without methylation adaptation, and it leads to fast and complete aggregation toward the most favorable…
We introduce a generic, purely mechanical model for environment sensitive motion of mammalian cells that is applicable to chemotaxis, haptotaxis, and durotaxis as modes of motility. It is able to theoretically explain all relevant…
Multicellular chemotaxis can occur via individually chemotaxing cells that are mechanically coupled. Alternatively, it can emerge collectively, from cells chemotaxing differently in a group than they would individually. Here we consider…
The Keller-Segel model is a system of partial differential equations that describes the movement of cells or organisms in response to chemical signals, a phenomenon known as chemotaxis. In this study, we analyze a doubly parabolic…
Chemotaxis phenomena govern the directed movement of micro-organisms in response to chemical stimuli. In this paper, we investigate two Keller--Segel systems of reaction-advection-diffusion equations modeling chemotaxis on thin networks.…