Related papers: Branching processes and bacterial growth
Bacteriophages spreading through populations of bacteria offer relatively simple, tuneable systems for testing mathematical models of range expansion. However, such models typically assume a static state into which to expand, which is not…
We model an enclosed system of bacteria, whose motility-induced phase separation is coupled to slow population dynamics. Without noise, the system shows both static phase separation and a limit cycle, in which a rising global population…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links…
Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…
We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an…
The aim of the paper is to describe two models of Covid-19 infection dynamics. For this purpose a special class of branching processes with two types of individuals is considered. These models are intended to use only the observed daily…
We consider a general growth mechanism, which acts at cellular level and above (organs, systems and whole organisms). Using its mathematical representation, the growth equation, we study the growth and division mechanisms of amoeba and…
Living cells maintain size homeostasis by actively compensating for size fluctuations. Here, we present two stochastic maps that unify phenomenological models by integrating fluctuating single-cell growth rates and size-dependent noise…
Many areas of agriculture rely on honey bees to provide pollination services and any decline in honey bee numbers can impact on global food security. In order to understand the dynamics of honey bee colonies we present a discrete time…
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…
We construct a pathwise formulation of a growing population of cells, based on two different samplings of lineages within the population, namely the forward and backward samplings. We show that a general symmetry relation, called…
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene…
Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…
In this note we consider a branching Brownian motion (BBM) on $\mathbb{R}$ in which a particle at spatial position $y$ splits into two at rate $\beta y^2$, where $\beta>0$ is a constant. This is a critical breeding rate for BBM in the sense…
Multiple-type branching processes that model the spread of infectious diseases are investigated. In these stochastic processes, the disease goes through multiple stages before it eventually disappears. We mostly focus on the critical…
We introduce two stochastic chemostat models consisting in a coupled population-nutrient process reflecting the interaction between the nutrient and the bacterias in the chemostat with finite volume. The nutrient concentration evolves…
Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and…
We provide a Galton--Watson model for the growth of a bacterial population in the presence of antibiotics. We assume that bacterial cells either die or duplicate, and the corresponding probabilities depend on the concentration of the…
We study explosiveness of age-dependent branching processes describing the early stages of an epidemic-spread: both forward- and backward process are analysed. For the classical age-dependent branching process $(h,G)$, where the offspring…