Related papers: Fast-mode elimination in stochastic metapopulation…
Building upon kinetic theory approaches for multi-agent systems and generalising them to scenarios where the total mass of the system is not conserved, we develop a modelling framework for phenotype-structured populations that makes it…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death processes. Interactions can manifest through the birth dynamics,…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Finite-size fluctuations arising in the dynamics of competing populations may have dramatic influence on their fate. As an example, in this article, we investigate a model of three species which dominate each other in a cyclic manner.…
We propose a stationary system that might be regarded as a migration model of some population abandoning their original place of abode and becoming part of another population, once they reach the interface boundary. To do so, we show a…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
A class of stochastic vector-borne infectious disease models is derived and studied. The class type is determined by a general nonlinear incidence rate of the disease. The disease spreads in a highly random environment with variability from…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of…
In large clonal populations, several clones generally compete which results in complex evolutionary and ecological dynamics: experiments show successive selective sweeps of favorable mutations as well as long-term coexistence of multiple…
Understanding the dynamics of metapopulations close to extinction is of vital importance for management. Levins-like models, in which local patches are treated as either occupied or empty, have been used extensively for this purpose, but…
Theoretical studies have shown that stochasticity can affect the dynamics of ecosystems in counter-intuitive ways. However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the…
For years, a main focus of ecological research has been to better understand the complex dynamical interactions between species which comprise food webs. Using the connectance properties of a widely explored synthetic food web called the…
The usual Langevin approach to describe systems driven by noise fails to describe the long time behavior of systems with multiple attractors. The solution of the associated linear Fokker-Planck equation is always unique, even though it…
We consider a system of two stochastic differential equations (SDEs) with competing two-way interactions driven by Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a…
The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent…