Related papers: Results on the contact process with dynamic edges …
We study the contact process running in the one-dimensional lattice undergoing dynamical percolation, where edges open at rate $vp$ and close at rate $v(1-p)$. Our goal is to explore how the speed of the environment, $v$, affects the…
The one-dimensional kinetic contact process with parallel update is introduced and studied by Monte Carlo simulations. This process is proposed to describe the plant population replication and epidemic disease spreading among them. The…
The renewal contact process, introduced in $2019$ by Fontes, Marchetti, Mountford, and Vares, extends the Harris contact process in $\mathbb{Z}^d$ by allowing the possible cure times to be determined according to independent renewal…
We consider contact processes on the hierarchical group, where sites infect other sites at a rate depending on their hierarchical distance, and sites become healthy with a constant recovery rate. If the infection rates decay too fast as a…
We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of…
Motivated by questions regarding long range percolation, we investigate a non-Markovian analogue of the Harris contact process in $\mathbb{Z}^d$: an individual is attached to each site $x \in \mathbb{Z}^d$, and it can be infected or…
We investigate a non-Markovian analogue of the Harris contact process in a finite connected graph G=(V,E): an individual is attached to each site x in V, and it can be infected or healthy; the infection propagates to healthy neighbors just…
We study the contact process in the regime of small infection rates on finite scale-free networks with stationary dynamics based on simultaneous updating of all connections of a vertex. We allow the update rates of individual vertices to…
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,…
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…
Recently, by introducing the notion of cumulatively merged partition, M\'enard and Singh provide a sufficient condition on graphs ensuring that the critical value of the contact process is positive. In this note, we show that the…
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.…
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…
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 $n$…
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…
We give a construction of a tree in which the contact process with any positive infection rate survives but, if a certain privileged edge $e^*$ is removed, one obtains two subtrees in which the contact process with infection rate smaller…
In this note we give a new method for getting a series of approximations for the extinction probability of the one-dimensional contact process by using the Gr\"obner basis.
We study a one-dimensional contact process with two infection parameters, one giving the infection rates at the boundaries of a finite infected region and the other one the rates within that region. We prove that the critical value of each…
We define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by linear preferential attachment. We consider a sequence of edge…
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…