Related papers: Long time behaviour of continuous-state nonlinear …
The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time,…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since the population size has no natural upper limit, this leads to systems in which there are…
We consider Markov jump processes describing structured populations with interactions via density dependance. We propose a Markov construction with a distinguished individual which allows to describe the random tree and random sample at a…
In this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
In this paper we study the long term evolution of a continuous time Markov chain formed by two interacting birth-and-death processes. The interaction between the processes is modelled by transition rates which are functions with suitable…
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…
We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the population. Parasites multiply randomly…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…
We develop a stochastic framework for viral population dynamics at the cellular level that explicitly incorporates the replication cycle with random stage durations. The model is formulated as a structured birth-death process coupled with a…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
Density dependent Markov population processes in large populations of size $N$ were shown by Kurtz (1970, 1971) to be well approximated over finite time intervals by the solution of the differential equations that describe their average…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…
We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…