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We refine previous results concerning the Renewal Contact Processes. We significantly widen the family of distributions for the interarrival times for which the critical value can be shown to be strictly positive. The result now holds for…

Probability · Mathematics 2026-02-02 Luiz Renato Fontes , Thomas S. Mountford , Daniel Ungaretti , Maria Eulália Vares

Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process (CP) where the contagion is expanded at…

Computational Physics · Physics 2010-02-19 S. Gomez , A. Arenas , J. Borge-Holthoefer , S. Meloni , Y. Moreno

We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…

Statistical Mechanics · Physics 2015-05-13 R. Juhász , G. Ódor

We study the contact process on the complete graph on $n$ vertices where the rate at which the infection travels along the edge connecting vertices $i$ and $j$ is equal to $ \lambda w_i w_j / n$ for some $\lambda >0$, where $w_i$ are i.i.d.…

Probability · Mathematics 2016-06-14 Jonathon Peterson

Bootstrap Percolation is a process defined on a graph which begins with an initial set of infected vertices. In each subsequent round, an uninfected vertex becomes infected if it is adjacent to at least $r$ previously infected vertices. If…

Combinatorics · Mathematics 2023-09-26 Hudson LaFayette , Rayan Ibrahim , Kevin McCall

In this paper we are concerned with contact processes on open clusters of oriented percolation in $Z^d$, where the disease spreads along the direction of open edges. We show that the two critical infection rates in the quenched and annealed…

Probability · Mathematics 2014-08-05 Xiaofeng Xue

The boundary modified contact process models an epidemic spreading in one dimension with two infection parameters, $\lambda_i$ and $\lambda_e$. Starting from a finite infected set, each edge of $\mathbb{Z}$ transmits the infection at rate…

Probability · Mathematics 2025-12-05 Andrew Heeszel

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

For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution…

Probability · Mathematics 2011-01-10 J. van den Berg

We study percolation properties of the upper invariant measure of the contact process on $\mathbb{Z}^d$. Our main result is a sharp percolation phase transition with exponentially small clusters throughout the subcritical regime and a…

Probability · Mathematics 2020-08-05 Thomas Beekenkamp

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

Digital contact tracing plays a crucial role in alleviating an outbreak, and designing multilevel digital contact tracing for a country is an open problem due to the analysis of large volumes of temporal contact data. We develop a…

Data Structures and Algorithms · Computer Science 2024-05-21 Gautam Mahapatra , Priodyuti Pradhan , Abhinandan Khan , Sanjit Kumar Setua , Rajat Kumar Pal , Ayush Rathor

Inspired by dengue and yellow fever epidemics, we investigated the contact process (CP) in a multiscale network constituted by one-dimensional chains connected through a Barab\'asi-Albert scale-free network. In addition to the CP dynamics…

Physics and Society · Physics 2011-01-07 Silvio C. Ferreira , Marcelo M. Martins

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

Periodically sheared colloids at low densities demonstrate a dynamical phase transition from an inactive to active phase as the strain amplitude is increased. The inactive phase consists of no collisions/contacts between particles in the…

Statistical Mechanics · Physics 2015-06-15 S. -L. -Y. Xu , J. M. Schwarz

The renewal contact process is a non-Markovian variant of the classical contact process in which recoveries are governed by independent renewal processes with interarrival distribution $\mu$. We establish new sufficient conditions ensuring…

Probability · Mathematics 2026-05-29 Gustavo O. de Carvalho , Lucas R. de Lima

The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory.…

Statistical Mechanics · Physics 2009-11-13 S. V. Fallert , Y. M. Kim , C. J. Neugebauer , S. N. Taraskin

We study the contact process on random graphs with low infection rate $\lambda$. For random $d$-regular graphs, it is known that the survival time is $O(\log n)$ below the critical $\lambda_c$. By contrast, on the Erd\H{o}s-R\'enyi random…

Probability · Mathematics 2024-12-31 Oanh Nguyen , Allan Sly

Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…

Probability · Mathematics 2020-03-16 Laurent Ménard , Arvind Singh

We consider a contact process on $Z^d$ with two species that interact in a symbiotic manner. Each site can either be vacant or occupied by individuals of species $A$ and/or $B$. Multiple occupancy by the same species at a single site is…

Probability · Mathematics 2019-12-11 Rick Durrett , Dong Yao