相关论文: Spreading with immunization in high dimensions
We introduce the effect of site contamination in a model for spatial epidemic spread and show that the presence of site contamination may have a strict effect on the model in the sense that it can make an otherwise subcritical process…
Social reinforcement and modular structure are two salient features observed in the spreading of behavior through social contacts. In order to investigate the interplay between these two features, we study the generalized epidemic process…
We identify the asymptotic distribution of the chemical distance in high-dimensional critical Bernoulli percolation. Namely, we show that the distance between the origin and a distant vertex conditioned to lie in the cluster of the origin…
We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the…
The probability distributions of the order parameter for two models in the directed percolation universality class were evaluated. Monte Carlo simulations have been performed for the one-dimensional generalized contact process and the…
We study bootstrap percolation processes on random simplicial complexes of some fixed dimension $d \geq 3$. Starting from a single simplex of dimension $d$, we build our complex dynamically in the following fashion. We introduce new…
Despite great progress in the study of critical percolation on $\mathbb{Z}^d$ for $d$ large, properties of critical clusters in high-dimensional fractional spaces and boxes remain poorly understood, unlike the situation in two dimensions.…
In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the…
The study of interdependent networks, and in particular the robustness on networks, has attracted considerable attention. Recent studies mainly assume that the dependence is fully interdependent. However, targeted attack for partially…
Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the…
We study a hierarchy of directed percolation (DP) processes for particle species A, B, ..., unidirectionally coupled via the reactions A -> B, ... When the DP critical points at all levels coincide, multicritical behavior emerges, with…
We consider the Diffusive Epidemic Process (DEP), a two-species reaction-diffusion process originally proposed to model disease spread within a population. This model exhibits a phase transition from an active epidemic to an absorbing state…
We present a finite-size scaling theory of a contact process with permanent immunity on uncorrelated scale-free networks. We model an epidemic outbreak by an analog of the susceptible-infected-removed model where an infected individual…
The behavior at criticality of spatial SIR (susceptible/infected/recovered) epidemic models in dimensions two and three is investigated. In these models, finite populations of size N are situated at the vertices of the integer lattice, and…
Based on the field theoretic formulation of the general epidemic process we study logarithmic corrections to scaling in dynamic isotropic percolation at the upper critical dimension d=6. Employing renormalization group methods we determine…
The way diseases spread through schools, epidemics through countries, and viruses through the Internet is crucial in determining their risk. Although each of these threats has its own characteristics, its underlying network determines the…
We consider the class of SIS epidemic models in which a large population of individuals chooses whether to adopt protection or to remain unprotected as the epidemic evolves. For a susceptible individual, adopting protection reduces the…
Infectious pathogens often propagate by superspreading, which focusses onward transmission on disproportionately few infected individuals. At the same time, infector-infectee pairs tend to have more similar transmission potentials than…
We study a susceptible-infected-removed (SIR) model with multiple seeds on a regular random graph. Many researchers have studied the epidemic threshold of epidemic models above which a global outbreak can occur, starting from an…
By bootstrap percolation we mean the following deterministic process on a graph $G$. Given a set $A$ of vertices "infected" at time 0, new vertices are subsequently infected, at each time step, if they have at least $r\in\mathbb{N}$…