Related papers: Viral Evolution and Adaptation as a Multivariate B…
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 sustainable use of multicomponent treatments such as combination therapies, combination vaccines/chemicals, and plants carrying multigenic resistance requires an understanding of how their population-wide deployment affects the speed of…
RNA viruses exist in large intra-host populations which display great genotypic and phenotypic diversity. We analyze a model of viral competition between two different viral strains infecting a constantly replenished cell pool, in which we…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
We propose and analyze a new class of controlled multi-type branching processes with a per-step linear resource constraint, motivated by potential applications in viral marketing and cancer treatment. We show that the optimal exponential…
In this work we propose a measure-valued stochastic process representing the dynamics of a virus population, structured by phenotypic traits and geographical space, and where viruses are transported between spatial locations by mechanical…
We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large…
This paper presents a stochastic model motivated by the study of a virus-like evolving population with different mutation rates. This is a continuous time birth-death model: the birth processes are mutually-exciting Hawkes processes and the…
The adaptive immune system engages in an arms race with evolving viruses, trying to generate new responses to viral strains that continually move away from the set of variants that have already elicited a functional immune response. In…
Viruses evolve in the background of host immune systems that exert selective pressure and drive viral evolutionary trajectories. This interaction leads to different evolutionary patterns in antigenic space. Examples observed in nature…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
Ben-Ari and Schinazi (2016) introduced a stochastic model to study `virus-like evolving population with high mutation rate'. This model is a birth and death model with an individual at birth being either a mutant with a random fitness…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
Microbial populations adapt to their environment by acquiring advantageous mutations, but in the early twentieth century, questions about how these organisms acquire mutations arose. The experiment of Salvador Luria and Max Delbr\"uck that…
Gene transcription is a highly stochastic and dynamic process. As a result, the mRNA copy number of a given gene is heterogeneous both between cells and across time. We present a framework to model gene transcription in populations of cells…
Gene-sharing networks provide a powerful framework to study the evolution of viruses and mobile genetic elements. These bipartite networks, which link genes to the genomes that contain them, exhibit characteristic degree distributions: a…
We analyze evolutionary dynamics in a confluent, branching cellular population, such as in a growing duct, vasculature, or in a branching microbial colony. We focus on the coarse-grained features of the evolution and build a statistical…