Related papers: Cellular replication limits in the Luria-Delbr\"uc…
We study supercritical age-structured branching models starting from a single particle with a random lifetime, where the reproduction law depends on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth…
In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
We propose a simple dynamic model of cancer development that captures carcinogenesis and subsequent cancer progression. A central idea of the model is to include the immune system as an extinction threshold, similar to the strong Allee…
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…
As cell proliferation is limited due to the loss of telomere repeats in DNA of normal somatic cells during division, telomere attrition can possibly play an important role in determining the maximum life span of organisms as well as…
We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
Objectives: In this study, we quantify the growth variability of tumour cell clones from a human leukemia cell line. Materials and methods: We have used microplate spectrophotometry to measure the growth kinetics of hundreds of individual…
For the model of periodic chronic myelogenous leukemia considered by Pujo-Menjouet, Mackey et al., model consisting of two delay differential equations, the equation for the density of so-called "resting cells" was studied from numerical…
In a previous paper we have introduced a phenomenological model of cell metabolism and of the cell cycle to simulate the behavior of large tumor cell populations (Chignola R and Milotti E, Phys. Biol. 2 (2005) 8-22). Here we describe a…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
Recent experimental evidence suggests that acute myeloid leukemias may originate from multiple clones of malignant cells. Nevertheless it is not known how the observed clones may differ with respect to cell properties such as proliferation…
In this study, we present a stochastic simulation model designed to explicitly incorporate cell cycle length, overcoming limitations associated with classical compartmental models. Our approach employs a delay mechanism to represent the…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
Cell division times in microbial populations display significant fluctuations, that impact the population growth rate in a non-trivial way. If fluctuations are uncorrelated among different cells, the population growth rate is predicted by…
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…
The main purpose of this work is the mathematical modelling of large populations of cells under different deterministic interactions among themselves, in balance with naturally random diffusion. We focus on cell-cell adhesion mechanisms for…
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…
The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…