Related papers: Extinction time of the logistic process

In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…

Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterize…

We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite…

Understanding the statistical properties of a collection of individuals subject to random displacements and birth-and-death events is key to several applications in physics and life sciences, encompassing the diagnostic of nuclear reactors…

We study a Markov birth-and-death process on a space of locally finite configurations, which describes an ecological model with a density dependent fecundity regulation mechanism. We establish existence and uniqueness of this process and…

This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental stochastic fluctuations and is in the form of a stochastic…

We analyze the influence of long-range correlated (colored) external noise on extinction phase transitions in growth and spreading processes. Uncorrelated environmental noise (i.e., temporal disorder) was recently shown to give rise to an…

This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…

Recently, a first step was made by the authors towards a systematic investigation of the effect of reaction-step-size noise - uncertainty in the step size of the reaction - on the dynamics of stochastic populations. This was done by…

Motivated by the paradigm of a super-Maltusian population catastrophe, we study a simple stochastic population model which exhibits a finite-time blowup of the population size and is strongly affected by intrinsic noise. We focus on the…

We establish connections between the absorption probabilities of a class of birth-death processes with killing, and the stationary tail of a related class of birth-death processes with catastrophes. The major ingredients of the proofs are a…

The evolution of several physical and biological systems, ranging from neutron transport in multiplying media to epidemics or population dynamics, can be described in terms of branching exponential flights, a stochastic process which…

The neutron population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to…

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle…

Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction.The…

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…

A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…

We introduce a new model for large scale evolution and extinction in which species are organized into food chains. The system evolves by two processes: origination/speciation and extinction. In the model, extinction of a given species can…

This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current…

The extinction of species is a major problem of concern with a large literature. Our investigation gives insight into when species extinctions must occur, with an emphasis on determining which species might possibly die out and on how fast…