Related papers: Generalized contact process on random environments
The adoption of individual behavioural patterns is largely determined by stimuli arriving from peers via social interactions or from external sources. Based on these influences, individuals are commonly assumed to follow simple or complex…
We study a spatial network model with exponentially distributed link-lengths on an underlying grid of points, undergoing a structural crossover from a random, Erd\H{o}s--R\'enyi graph to a $2D$ lattice at the characteristic interaction…
In the multitype contact process, vertices of a graph can be empty or occupied by a type 1 or a type 2 individual; an individual of type $i$ dies with rate 1 and sends a descendant to a neighboring empty site with rate $\lambda_i$. We study…
We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the…
This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a…
The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection eventually dies out. For larger lambda the…
We seek models for the genotype evolution of agricultural animals, animals involved in primary production processes. Classical models for genotype evolution have tended to be very simple in order that analytic methods may be employed in…
The contact process with diffusion (PCPD) defined by the binary reactions 2 B -> 3 B, 2 B -> 0 and diffusive particle spreading exhibits an unusual active to absorbing phase transition whose universality class has long been disputed.…
In the system we study, 1's and 0's represent occupied and vacant sites in the contact process with births at rate $\lambda$ and deaths at rate 1. $-1$'s are sterile individuals that do not reproduce but appear spontaneously on vacant sites…
Contact tracing can be thought of as a race between two processes: an infection process and a tracing process. In this paper, we study a simple model of infection spreading on a tree, and a tracer who stabilizes one node at a time. We focus…
We propose a mean-field (MF) approximation for the recurrence relation governing the dynamics of $m$ species of particles on a square lattice, and we simultaneously perform Monte Carlo (MC) simulations under identical initial conditions to…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
We introduce a multitype contact process with temporal heterogeneity involving two species competing for space on the $d$-dimensional integer lattice. Time is divided into seasons called alternately season 1 and season 2. We prove that…
We consider the critical branching processes in correlated random environment which is positively associated and study the probability of survival up to the n-th generation. Moreover, when the environment is given by fractional Brownian…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…
We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals $i$ and $j$ is…