Related papers: A cell-cell repulsion model on a hyperbolic Keller…
This paper investigates an initial-Neumann boundary value problem for a Keller--Segel system with parabolic-parabolic-ODE coupling. The model incorporates a signal-dependent, non-increasing motility function that, through indirect signal…
In multicellular organisms, several cell states coexist. For determining each cell type, cell-cell interactions are often essential, in addition to intracellular gene expression dynamics. Based on dynamical systems theory, we propose a…
This paper investigates the incompressible limit of a system modelling the growth of two cells population. The model describes the dynamics of cell densities, driven by pressure exclusion and cell proliferation. It has been shown that…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
The entanglement of population dynamics, evolution, and adaptive radiation for species competing for resources is studied. For resource harvesting, we modify the model used in Ref. Phys. Rev. Lett. 118 048103 and introduce new resource…
Cycling tissues such as the intestinal epithelium, germ line, and hair follicles, require a constant flux of differentiated cells. These tissues are maintained by a population of stem cells, which generate differentiated progenies and…
The evolution of a chemotactic system involving a population of cells attracted to self-produced chemicals is described by the Keller-Segel system. In spacial dimension 2, this system demonstrates a balance between the spreading effect of…
This paper develops a quasispecies model where cells can adopt a two-cell survival strategy. Within this strategy, pairs of cells join together, at which point one of the cells sacrifices its own replicative ability for the sake of the…
The progression of a cell population where each individual is characterized by the value of an internal variable varying with time (e.g. size, weight, and protein concentration) is typically modeled by a Population Balance Equation, a first…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
Bet-hedging is a phenotype diversification strategy that combines a fast-growing vulnerable phenotype with a slow-growing resistant phenotype. In environments switching between favorable and unfavorable conditions, bet-hedging optimizes…
The understanding of the macroscopic phenomenological models of the population growth at a microscopic level is important to predict the population behaviors emerged from the interactions between the individuals. In this work we consider…
We propose a model for evolution aiming to reproduce statistical features of fossil data, in particular the distributions of extinction events, the distribution of species per genus and the distribution of lifetimes, all of which are known…
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak…
The immune response to a pathogen has two basic features. The first is the expansion of a few pathogen-specific cells to form a population large enough to control the pathogen. The second is the process of differentiation of cells from an…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
The Keller-Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form, it is a conservative drift-diffusion equation for the cell density coupled to an…
Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the…
We investigate a partial differential equation model of a cancer cell population, which is structured with respect to age and telomere length of cells. We assume a continuous telomere length structure, which is applicable to the clonal…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…