Related papers: First-passage competition with different speeds: p…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…
Given a discrete-time non-lattice supercritical branching random walk in $\mathbb{R}^d$, we investigate its first passage time to a shifted unit ball of a distance $x$ from the origin, conditioned upon survival. We provide precise…
Classical understanding of the outcome of the struggle for existence results in the Darwinian survival of the fittest. Here we show that the situation may be different, more complex and arguably more interesting. Specifically, we show that…
We consider the time evolution of two-dimensional Levy flights in a finite area with periodic boundary conditions. From simulations we show that the fractal path dimension d_f and thus the degree of area coverage grows in time until it…
We consider expanding maps such that the unit interval can be represented as a full symbolic shift space with bounded distortion. There are already theorems about the Hausdorff dimension for sets defined by the set of accumulation points…
Infectious diseases outbreaks are often characterized by a spatial component induced by hosts' distribution, mobility, and interactions. Spatial models that incorporate hosts' movements are being used to describe these processes, to…
In this work, we provide some novel results that establish both the existence of Henig global proper efficient points and their density in the efficient set for vector optimization problems in arbitrary normed spaces. Our results do not…
Different strains competing for a common pool of susceptible individuals is a key problem in mathematical epidemiology. To address this problem, we investigate a two-strain model within a Susceptible-Infected-Recovered (SIR) framework.…
Let $\mathcal{M}$ be a set with $M$ elements, let $\psi :\mathcal{M}\to\mathcal{M}$ be a bijective involution, and let~$\boldsymbol{\mathcal{X}}_{\psi}$ be the set of sequences $(x_1,\dots,x_M)\in\mathcal{M}^M$ with the property that…
We study first-passage percolation in two dimensions, using measures mu on passage times with b:=inf supp(mu) >0 and mu({b})=p \geq p_c, the threshold for oriented percolation. We first show that for each such mu, the boundary of the limit…
We study a system of PDEs modeling the population dynamics of two competitive species whose spatial movements are governed by both diffusion and mutually repulsive chemotaxis effects. We prove that solutions to this system are globally…
We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \mu. In addition, there is an aggregate, which…
Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the…
We investigate the effect on survival and coexistence of introducing forest fire epidemics to a certain two-species competition model. The model is an extension of the one introduced by Durrett and Remenik [DR09], who studied a discrete…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case…
The two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity, it is known that there is a positive probability for…
The transition from localized to systemic spreading of bacteria, viruses and other agents is a fundamental problem that spans medicine, ecology, biology and agriculture science. We have conducted experiments and simulations in a simple…
The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator,…
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…