Related papers: Minimizing the population extinction risk by migra…

This paper is concerned with spatial spreading dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species will become extinct in the habitat once the…

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…

We discuss two cases that can be connected to the dynamics of interacting populations: (I.) density waves for the case or negligible random fluctuations of the populations densities, and (II.) probability distributions connected to the…

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…

As infectious disease outbreaks emerge, public health agencies often enact vaccination and social distancing measures to slow transmission. Their success depends on not only strategies and resources, but also public adherence. Individual…

We consider a spatial branching process with emigration in which children either remain at the same site as their parents or migrate to new locations and then found their own colonies. We are interested in asymptotics of the partition of…

Both cooperation and migration are ubiquitous in human society and animal world. In this Rapid Communication, we propose an aspiration-induced migration in which individuals will migrate to new sites provided that their payoffs are below…

While social living is considered to be an indispensable part of human life in today's ever-connected world, social distancing has recently received much public attention on its importance since the outbreak of the coronavirus pandemic. In…

We study the effect of mutations in a simple model of colonization, based on Montecarlo simulations. When the population colonizes the whole available habitat, a maximum population density is reached, which depends on the mutation rate.…

This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…

Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a…

An integro-differential equation on a tree graph is used to model the evolution and spatial distribution of a population of organisms in a river network. Individual organisms become mobile at a constant rate, and disperse according to an…

A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…

Containing an epidemic at its origin is the most desirable mitigation. Epidemics have often originated in rural areas, with rural communities among the first affected. Disease dynamics in rural regions have received limited attention, and…

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic Susceptible-Infected-Susceptible model, we predict the distribution of large…

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset $\Omega$ of Euclidean space. The approximation is good when a large number of…

We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the…

We consider a population spreading across a finite number of sites. Individuals can move from one site to the other according to a network (oriented links between the sites) that vary periodically over time. On each site, the population…

Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, provided that the total…

We consider the problem of constructing public facilities, such as hospitals, airports, or malls, in a country with a non-uniform population density, such that the average distance from a person's home to the nearest facility is minimized.…