Related papers: Stochastic modeling of in vitro bactericidal poten…
Since the last century, deterministic compartmental models have emerged as powerful tools to predict and control epidemic outbreaks, in many cases helping to mitigate their impacts. A key quantity for these models is the so-called Basic…
Falciparum malaria is a major parasitic disease causing widespread morbidity and mortality globally. Artemisinin derivatives---the most effective and widely-used antimalarials that have helped reduce the burden of malaria by 60% in some…
We propose a computational framework to study the growth and spread of bacterial biofilms on interfaces, as well as the action of antibiotics on them. Bacterial membranes are represented by boundaries immersed in a fluid matrix and subject…
New automated and high-throughput methods allow the manipulation and selection of numerous bacterial populations. In this manuscript we are interested in the neutral diversity patterns that emerge from such a setup in which many bacterial…
Williams and Bjerknes proposed a simple stochastic growth model to describe the tumor growth in the basal layer of an epithelium. In this work we generalize this model by including the possibility of saturation in the tumor growth as it is…
This work develops further a probabilist approach to the asymptotic behavior of growth-fragmentation semigroups via the Feynman-Kac formula, which was introduced in a joint article with A.R. Watson [4]. Here, it is first shown that the…
The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…
The growth of a population is often modeled as branching process where each individual at the end of its life is replaced by a certain number of offspring. An example of these branching models is the Bellman-Harris process, where the…
The large reservoir of antibiotic resistant bacteria in raw and treated water supplies is a matter of public health concern. Currently, the National Antimicrobial Resistance Monitoring Systems, a collaborative effort of the Centers for…
We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyse a version of such models…
Present study is dedicated to the problem of electrochemical analysis of multicomponent mixtures such as milk. A combination of cyclic voltammetry facilities and machine learning technique made it possible to create a pattern recognition…
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the…
Ordinary differential equation (ODE) models used in mathematical epidemiology assume explicitly or implicitly large populations. For the study of infections in a hospital this is an extremely restrictive assumption as typically a hospital…
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,…
A stochastic model for the growth of a virus in a cell population is introduced. The virus has two ways of spreading: either by allowing its host cell to live on and duplicate, or else by multiplying in large numbers within the host cell…
Mathematical models have been widely used to describe the collective movement of bacteria by chemotaxis. In particular, bacterial concentration waves traveling in a narrow channel have been experimentally observed and can be precisely…
Motivated by the problem of estimating the bacterial growth rates for genome assemblies from shotgun metagenomic data, we consider the permuted monotone matrix model $Y=\Theta\Pi+Z$, where $Y\in \mathbb{R}^{n\times p}$ is observed,…
The growth-fragmentation equation models systems of particles that grow and reproduce as time passes. An important question concerns the asymptotic behaviour of its solutions. Bertoin and Watson ($2018$) developed a probabilistic approach…
Bacteria evolve resistance to antibiotics by a multitude of mechanisms. A central, yet unsolved question is how resistance evolution affects cell growth at different drug levels. Here we develop a fitness model that predicts growth rates of…
In this paper, we consider a flocculation model in a chemostat where one species is present in two forms: planktonic and aggregated bacteria with the presence of a single resource. The removal rates of isolated and attached bacteria are…