Related papers: On the One-Dimensional Contact Process with Enhanc…

We investigate a modified one-dimensional contact process with varying infection rates. Specifically, the infection spreads at rate $\lambda_e$ along the boundaries of the infected region and at rate $\lambda_i$ elsewhere. We establish the…

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…

The basic contact process with parameter $\mu$ altered so that infections of sites that have not been previously infected occur at rate proportional to $\lambda$ instead is considered. Emergence of an infinite epidemic starting out from a…

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…

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…

In this work we study the one-dimensional contact process with diffusion using two different approaches to research the critical properties of this model: the supercritical series expansions and finite-size exact solutions. With special…

We are concerned with the supercritical contact process modified so that first infection occurs at a lower rate, it is known that the process survives with positive probability. Regarding the rightmost infected of the process started from…

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…

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…

We show that the contact process on a random $d$-regular graph initiated by a single infected vertex obeys the "cutoff phenomenon" in its supercritical phase. In particular, we prove that when the infection rate is larger than the critical…

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…

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…

In this paper we are concerned with contact processes with random edge weights on rooted regular trees. We assign i.i.d weights on each edge on the tree and assume that an infected vertex infects its healthy neighbor at rate proportional to…

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…

We consider a random walk on top of the contact process on $\mathbb{Z}^d$ with $d\geq 1$. In particular, we focus on the "contact process as seen from the random walk". Under the assumption that the infection rate of the contact process is…

The contact process on dynamic edges (CPDE) is a contact process evolving on a dynamic environment given by a dynamical percolation on the edges of Z d\,: each edge updates its state to open or closed with respective rates vp and v(1 -p).…

This paper gives a new, simple proof of the known fact that for contact processes on general lattices, in the subcritical regime the expected number of infected sites decays exponentially fast as time tends to infinity. The proof also…

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…

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…

In this paper we are concerned with the two-stage contact process on the lattice $\mathbb{Z}^d$ introduced in \cite{Krone1999}. We gives a limit theorem of the critical infection rate of the process as the dimension $d$ of the lattice grows…