Related papers: Explicit formulas for a continuous stochastic matu…
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
We consider a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects which is introduced in [2]. It is comprised of phase-field equation to describe tumor growth, which is coupled to a…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…
We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The…
We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…
We exhibit a stochastic discrete time model that has exactly the Eigen model as its deterministic continuous limit. Such model can be divided into two phases: reproduction followed by neutral selection. This result suggests that Eigen model…
In this paper, we first propose a new extended mixture model of residual lifetime distributions. We show that this model is suitable in modeling residual lifetime in some practical situations. Several closure properties of some well-known…
The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
Cancer progression and monotonic accumulation models were developed to discover dependencies in the irreversible acquisition of binary traits from cross-sectional data. They have been used in computational oncology and virology but also in…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…
Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states,…
In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak…
Applications of first passage times in stochastic processes arise across a wide range of length and time scales in biological settings. After an initial technical overview, we survey representative applications and their corresponding…