Related papers: Mutation frequencies in a birth-death branching pr…
We consider an expanding population on the plane. The genealogy of a sample from the population is modelled by coalescing Brownian motion on the circle. We establish a weak law of large numbers for the site frequency spectrum in this model.…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
Assume that individuals alive at time $t$ in some population can be ranked in such a way that the coalescence times between consecutive individuals are i.i.d. The ranked sequence of these branches is called a coalescent point process. We…
Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis.…
The ability to estimate how a tumor might evolve in the future could have tremendous clinical benefits, from improved treatment decisions to better dose distribution in radiation therapy. Recent work has approached the glioma growth…
We consider a two-type reducible branching Brownian motion, defined as a particle system on the real line in which particles of two types move according to independent Brownian motions and create offspring at a constant rate. Particles of…
There are numerous stochastic models for cancer risk for a given tissue. Many rely on the following two hypotheses. 1. There is a fixed probability that a given cell division will eventually lead to a cancerous cell. 2. Cell divisions are…
In the present article we demonstrate a new hybrid model of tumor growth. Our model is stochastic by tumor population development and strongly deterministic in cell motility dynamics and spatial propagation. In addition, it has excellent…
We study a mutation-selection model with a fluctuating environment. More precisely, individuals in a large population are assumed to have a modifier locus determining the mutation rate $u \in [0,\vartheta]$ at a second locus with types $v…
In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investigate a phenotype-structured model of solid tumour growth in…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…
We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
This paper explores the Site Frequency Spectrum (SFS) in stationary branching populations. We derive estimates for the SFS associated with a sample from a continuous-state branching process conditioned to never go extinct, utilizing a…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
Despite initial success, cancer therapies often fail due to the emergence of drug-resistant cells. In this study, we use a mathematical model to investigate how cancer evolves over time, specifically focusing on the state of the tumor when…
Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not…
We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute the time evolution of quantities such as the mean and…
We study a stochastic branching model for a population structured by a quantitative phenotypic trait and subject to births, deaths, and mutations. In a regime of large population and small mutations, and in logarithmic scales of size and…