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Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…

Probability · Mathematics 2015-08-27 Kevin Kuoch

In order to understand the cost of a potentially high infectiousness of symptomatic individuals or, on the contrary, the benefit of social distancing, quarantine, etc. in the course of an infectious disease, this paper considers a natural…

Probability · Mathematics 2024-04-29 Lamia Belhadji , Nicolas Lanchier , Max Mercer

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

In this paper, we derive a precise estimate for the mean extinction time of the contact process with a fixed infection rate on a star graph with $N$ leaves. Specifically, we determine not only the exponential main factor but also the exact…

Probability · Mathematics 2026-02-05 Younghun Jo

We study the contact process on the long-range percolation cluster on $\mathbb{Z}$ where each edge $\langle i,j \rangle$ is open with probability $|i-j|^{-s}$ for $s> 2$. Using a renormalization procedure we apply Peierls-type argument to…

Probability · Mathematics 2026-03-17 Pablo A. Gomes , Marcelo R. Hilário , Bernardo N. B. de Lima , Thomas Mountford

We consider the contact process with infection rate $\lambda$ on a random $(d+1)$-regular graph with $n$ vertices, $G_n$. We study the extinction time $\tau_{G_n}$ (that is, the random amount of time until the infection disappears) as $n$…

Probability · Mathematics 2014-05-06 Jean-Christophe Mourrat , Daniel Valesin

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

The contact process is a simple infection spreading model showcasing an out-of-equilibrium phase transition between a macroscopically active and an inactive phase. Such absorbing state phase transitions are often sensitive to the presence…

Statistical Mechanics · Physics 2025-09-22 Leone V. Luzzatto , Juan Felipe Barrera López , István A. Kovács

The pair contact process with diffusion is studied by means of multispin Monte Carlo simulations and density matrix renormalization group calculations. Effective critical exponents are found to behave nonmonotonically as functions of time…

Statistical Mechanics · Physics 2009-11-10 G. T. Barkema , E. Carlon

We study the supercritical contact process on Galton-Watson trees and periodic trees. We prove that if the contact process survives weakly then it dominates a supercritical Crump-Mode-Jagers branching process. Hence the number of infected…

Probability · Mathematics 2019-12-12 Xiangying Huang

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

Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent…

Disordered Systems and Neural Networks · Physics 2009-11-07 Gyorgy Szabo , Hajnalka Gergely , Beata Oborny

We analyze the properties of the contact process with long-range interactions by the use of a kinetic ensemble in which the total number of particles is strictly conserved. In this ensemble, both annihilation and creation processes are…

Statistical Mechanics · Physics 2009-11-13 Carlos E. Fiore , Mário J. de Oliveira

We introduce and study the mutating contact process, a variant of the multitype contact process, where one type mutates at a constant rate to the other type. We prove that on $\mathbb{Z}$ a single mutant cannot survive while on…

Probability · Mathematics 2018-01-08 Idan Alter , Gideon Amir

We consider the contact process on a dynamic graph defined as a random $d$-regular graph with a stationary edge-switching dynamics. In this graph dynamics, independently of the contact process state, each pair $\{e_1,e_2\}$ of edges of the…

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

The long-time dynamics of the 1D contact process suddenly brought out of an uncorrelated initial state is studied through a light-cone transfer-matrix renormalisation group approach. At criticality, the system undergoes ageing which is…

Statistical Mechanics · Physics 2007-05-23 Tilman Enss , Malte Henkel , Alan Picone , Ulrich Schollwöck

We have studied the critical properties of the contact process on a square lattice with quenched site dilution by Monte Carlo simulations. This was achieved by generating in advance the percolating cluster, through the use of an appropriate…

Disordered Systems and Neural Networks · Physics 2017-05-24 Alexander H. O. Wada , Mário J. de Oliveira

We study the contact process on the configuration model with a power law degree distribution, when the exponent is smaller than or equal to two. We prove that the extinction time grows exponentially fast with the size of the graph and prove…

Probability · Mathematics 2015-07-20 Van Hao Can , Bruno Schapira

The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…

Probability · Mathematics 2026-03-11 Natalia Cardona-Tobón , Marcel Ortgiese , Marco Seiler , Anja Sturm