Related papers: A cell-cell repulsion model on a hyperbolic Keller…

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…

As a class of nonlinear partial differential equations, the Keller-Segel system is widely used to model chemotaxis in biology. In this paper, we present the construction and analysis of a decoupled linear, mass-conservative, block-centered…

The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…

Resistance to insecticide is considered nowadays one of the major threats to insect control, as its occurrence reduces drastically the efficiency of chemical control campaigns, and may also perturb the application of other control methods,…

This paper investigates the competition of two species in a heterogeneous environment subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are…

To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…

We consider a Keller-Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are less singular than Newtonian interaction. Here, the nonlinear diffusion is chosen…

There are numerous scenarios in which populations of cells migrate in crowded environments. Typical examples include wound healing, cancer growth and embryo development. In these crowded environments cells are able to interact with each…

Cancer cells co-cultured in vitro reveal unexpected differential growth rates that classical exponential growth models cannot account for. Two non-interacting cell lines were grown in the same culture, and counts of each species were…

The evolution of complex cellular life involved two major transitions: the encapsulation of self-replicating genetic entities into cellular units and the aggregation of individual genes into a collectively replicating genome. In this paper,…

Since the seminal work of Powell, the relationships between the population growth rate, the probability distributions of generation time, and the distribution of cell age have been known for the bacterial population in a steady state of…

Cell-cell adhesion is widely hypothesised to maintain cohesion within the long streams of follower cells that trail leader subpopulations during collective migration, including in neural crest cell migration, angiogenesis, and cancer cell…

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…

A novel mechanism for cell differentiation is proposed, based on the dynamic clustering in a globally coupled chaotic system. A simple model with metabolic reaction, active transport of chemicals from media, and cell division is found to…

The study of infectious disease propagation is essential for understanding and controlling epidemics. One of the most useful tools for gaining insights into the spread of infectious diseases is mathematical modelling. In terms of…

We study the properties of a semi-implicit Euler scheme that is widely used in time discretization of Keller-Segel equations both in the parabolic-elliptic form and the parabolic-parabolic form. We prove that this linear, decoupled,…

We study the combined effects of periodically varying carrying capacity and survival rates on the fish population in the ocean (sea). We introduce the Getz type delay differential equation model with a control parameter which describes how…

Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…

Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight…

This paper develops a point-mutation model describing the evolutionary dynamics of a population of adult stem cells. Such a model may prove useful for quantitative studies of tissue aging and the emergence of cancer. We consider two modes…