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Related papers: Contact processes on the integers

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We study the contact process with stirring on $\mathbb{Z}^d$. In this process, particles occupy vertices of $\mathbb{Z}^d$; each particle dies with rate 1 and generates a new particle at a randomly chosen neighboring vertex with rate…

Probability · Mathematics 2015-09-15 Anna Levit , Daniel Valesin

A class of non-local contact processes is introduced and studied using mean-field approximation and numerical simulations. In these processes particles are created at a rate which decays algebraically with the distance from the nearest…

Statistical Mechanics · Physics 2009-11-11 F. Ginelli , H. Hinrichsen , R. Livi , D. Mukamel , A. Torcini

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

In the present paper, we study the relation between criticality and information transmission in the one-dimensional contact process with infection parameter $\lambda .$ To do this we define the {\it sensitivity} of the process to its…

Probability · Mathematics 2017-11-01 Marzio Cassandro , Antonio Galves , Eva Löcherbach

We show results for the contact process on Barabasi networks. The contact process is a model for an epidemic spreading without permanent immunity that has an absorbing state. For finite lattices, the absorbing state is the true stationary…

Physics and Society · Physics 2022-01-24 D. S. M. Alencar , T. F. A. Alves , G. A. Alves , R. S. Ferreira , A. Macedo-Filho , F. W. S. Lima

We study the contact process on a dynamic random~$d$-regular graph with an edge-switching mechanism, as well as an interacting particle system that arises from the local description of this process, called the herds process. Both these…

Probability · Mathematics 2023-10-02 Bruno Schapira , Daniel Valesin

We consider the contact process with dormancy, where wake-up times follow a renewal process. Without infection between dormant individuals, we show that the process under certain conditions grows at most logarithmically. On the other hand,…

Probability · Mathematics 2025-03-06 Noemi Kurt , Michel Reitmeier , András Tóbiás

This paper is concerned with contact process with random vertex weights on regular trees, and study the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection…

Probability · Mathematics 2017-03-08 Yu Pan , Dayue Chen , Xiaofeng Xue

Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the…

Probability · Mathematics 2007-05-23 L. Belhadji , N. Lanchier

The stacked contact process is a three-state spin system that describes the co-evolution of a population of hosts together with their symbionts. In a nutshell, the hosts evolve according to a contact process while the symbionts evolve…

Probability · Mathematics 2020-05-06 Eric Foxall , Nicolas Lanchier

We investigate the contact process on four different types of scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where each potential edge is updated with a rate depending on the strength of the adjacent…

Probability · Mathematics 2022-06-03 Emmanuel Jacob , Amitai Linker , Peter Mörters

The stacked contact process is a stochastic model for the spread of an infection within a population of hosts located on the $d$-dimensional integer lattice. Regardless of whether they are healthy or infected, hosts give birth and die at…

Probability · Mathematics 2014-10-16 Nicolas Lanchier , Yuan Zhang

In this paper we will consider the contact process in a very simple type of random environment that physicists call the random dilution model. We start with the contact process on a graph, here either $\mathbb{Z}^d$, a $d$-dimensional torus…

Probability · Mathematics 2025-06-02 Rick Durrett

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

In this paper we introduce a contact process on a dynamical long range percolation (CPDLP) defined on a complete graph $(V,\mathcal{E})$. A dynamical long range percolation is a Feller process defined on the edge set $\mathcal{E}$, which…

Probability · Mathematics 2023-11-27 Marco Seiler , Anja Sturm

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 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 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

We show existence of a non-trivial phase transition for the contact process, a simple model for infection without immunity, on a network which reacts dynamically to the infection trying to prevent an epidemic. This network initially has the…

Probability · Mathematics 2023-12-12 John Fernley , Peter Mörters , Marcel Ortgiese

Contact processes describe the transmission of distinct properties of nodes via the links of a network. They provide a simple framework for many phenomena, such as epidemic spreading and opinion formation. Combining contact processes with…

Physics and Society · Physics 2010-11-12 Anne-Ly Do , Thilo Gross