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Related papers: Contact processes on the integers

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It has been proposed (Phys. Rev. E {\bf 71}, 026121 (2005)) that unlike the short range contact process, a long-range counterpart may lead to the existence a discontinuous phase transition in one dimension. Aiming at exploring such link,…

Statistical Mechanics · Physics 2013-06-14 Carlos E. Fiore , Mário J. de Oliveira

The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and…

Probability · Mathematics 2011-11-10 Erik I. Broman

We are interested in the spread of an epidemic between two communities that have higher connectivity within than between them. We model the two communities as independent Erdos-Renyi random graphs, each with n vertices and edge probability…

Probability · Mathematics 2012-10-15 David Sivakoff

Infectious diseases are practically represented by models with multiple states and complex transition rules corresponding to, for example, birth, death, infection, recovery, disease progression, and quarantine. In addition, networks…

Disordered Systems and Neural Networks · Physics 2007-05-23 Naoki Masuda , Norio Konno

We study two one-dimensional variants of the contact process: the contact-and-barrier process, where the population evolves in a region delimited by a randomly moving barrier, and the multitype contact process, in which two species compete…

Probability · Mathematics 2026-02-27 Isabella Alvarenga , Daniel Valesin

Propagation of contagion in networks depends on the graph topology. This paper is concerned with studying the time-asymptotic behavior of the extended contact processes on static, undirected, finite-size networks. This is a contact process…

Physics and Society · Physics 2015-07-03 June Zhang , José M. F. Moura

We study the contact process on a random bipartite connection hypergraph generated from two Poisson point processes, with mark-dependent connection thresholds. For asymmetric infection rates and asymmetric power law tail decays of the two…

Probability · Mathematics 2026-04-02 John Fernley , Christian Hirsch , Daniel Valesin

In this paper we are concerned with the contact process on the squared lattice. The contact process intuitively describes the spread of the infectious disease on a graph, where an infectious vertex becomes healthy at a constant rate while a…

Probability · Mathematics 2017-01-04 Xiaofeng Xue

We study the limiting behavior of an interacting particle system evolving on the lattice $Z^{d}$ for $d\ge 3$. The model is known as the contact process with rapid stirring. The process starts with a single particle at the origin. Each…

Probability · Mathematics 2019-01-31 Segev Shlomov , Leonid Mytnik

We study a version of first passage percolation on $\mathbb{Z}^d$ where the random passage times on the edges are replaced by contact times represented by random closed sets on $\mathbb{R}$. Similarly to the contact process without…

Probability · Mathematics 2026-02-02 Benedikt Jahnel , Lukas Lüchtrath , Anh Duc Vu

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…

Probability · Mathematics 2018-03-06 Thomas Mountford , Pedro Luis Barrios Pantoja , Daniel Valesin

In this article, we present two novel variants of the contact process. In the first variant individuals carry a viral load. An individual with viral load zero is classified as healthy and otherwise infected. If an individual becomes…

Probability · Mathematics 2026-02-20 Marco Seiler

We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [17] for vegetation patterns in arid landscapes, we focus on…

Probability · Mathematics 2014-09-17 J. van den Berg , J. E. Björnberg , M. Heydenreich

The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a non-equilibrium phase transition into an absorbing state that has been widely investigated and shown to…

Statistical Mechanics · Physics 2019-09-11 Federico Carollo , Edward Gillman , Hendrik Weimer , Igor Lesanovsky

We consider the contact process on the preferential attachment graph. The work of Berger, Borgs, Chayes and Saberi [BBCS1] confirmed physicists predictions that the contact process starting from a typical vertex becomes endemic for an…

Probability · Mathematics 2017-02-23 Van Hao Can

We consider a symmetric finite-range contact process on $\mathbb{Z}$ with two types of particles (or infections), which propagate according to the same supercritical rate and die (or heal) at rate $1$. Particles of type $1$ can enter any…

Probability · Mathematics 2022-02-22 Mariela Pentón Machado

We present general results for the contact process by a method which applies to all transitive graphs of bounded degree, including graphs of exponential growth. The model's infection rates are varied through a control parameter, for which…

Probability · Mathematics 2008-09-29 Michael Aizenman , Paul Jung

We study the effects of local and distance interactions in the unidimensional contact process (CP). In the model, each site of a lattice is occupied by an individual, which can be healthy or infected. As in the standard CP, each infected…

Statistical Mechanics · Physics 2019-01-30 Priscila R. Silveira , Marcelo M. de Oliveira , Sidiney G. Alves

This paper studies contact processes on general countable groups. It is shown that any such contact process has a well-defined exponential growth rate, and this quantity is used to study the process. In particular, it is proved that on any…

Probability · Mathematics 2008-08-28 Jan M. Swart

We study degree-penalized contact processes on Galton-Watson trees (GW) and the configuration model. The model we consider is a modification of the usual contact process on a graph. In particular, each vertex can be either infected or…

Probability · Mathematics 2026-01-21 Zsolt Bartha , Júlia Komjáthy , Daniel Valesin