Related papers: The asymmetric multitype contact process
We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the $d$-dimensional integer lattice and regular trees. We prove that for birth rates in a certain interval there is coexistence on…
We propose the following model for speciation and extinction. Birth and deaths occur according to spatially inhomogeneous contact rates. We assume that the ratio of the birth rate over the death rate at a site converges to some limit as the…
We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models. Under the assumption that the infection rate is above the critical value for the process on the…
The contact process with an asymptomatic state, introduced in [Belhadji, Lanchier and Mercer, Stochastic Process. Appl., 176:104417, 2024], is a natural variant of the basic contact process that distinguishes between asymptomatic (state 1)…
We introduce a two-type first passage percolation competition model on infinite connected graphs as follows. Type 1 spreads through the edges of the graph at rate 1 from a single distinguished site, while all other sites are initially…
In the two-type Richardson model on a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, each vertex is at a given time in state $0$, $1$ or $2$. A $0$ flips to a $1$ (resp.\ $2$) at rate $\lambda_1$ ($\lambda_2$) times the number of…
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…
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…
In this paper we study threshold-one contact processes on lattices and regular trees. The asymptotic behavior of the critical infection rates as the degrees of the graphs growing to infinity are obtained. Defining \lambda_c as the supremum…
We study a contact process running in a random environment in $\mathbb {Z}^d$ where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by…
We study the contact process in a dynamical random environment defined on the vertices and edges of a graph. For a broad class of processes, we establish an asymptotic shape theorem for the set H_t, which represents the vertices that have…
We consider the discrete-time threshold-$\theta \ge 2$ contact process on a random r-regular graph on n vertices. In this process, a vertex with at least \theta occupied neighbors at time t will be occupied at time t+1 with probability p,…
To study later spatial evolutionary games based on the multitype contact process, we first focus in this paper on the conditions for survival/extinction in the presence of only one strategy, in which case our model consists of a variant of…
There are two types of particles interacting on a homogeneous tree of degree d + 1. The particles of the first type colonize the empty space with exponential rate 1, but cannot take over the vertices that are occupied by the second type.…
We study two famous interacting particle systems, the so-called Richardson's model and the contact process, when we add a stirring dynamics to them. We prove that they both satisfy an asymptotic shape theorem, as their analogues without…
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…
We consider the contact process with infection rate $\lambda$ on $\mathbb{T}_n^d$, the $d$-ary tree of height $n$. We study the extinction time $\tau_{\mathbb{T}_n^d}$, that is, the random time it takes for the infection to disappear when…
It is known that the limiting behavior of the contact process strongly depends upon the geometry of the graph on which particles evolve: while the contact process on the regular lattice exhibits only two phases, the process on homogeneous…
We are interested in the spread of an epidemic between two communities that have higher connectivity within than between them. We model the two communities as independent Erdos-Renyi random graphs, each with n vertices and edge probability…
If we consider the contact process with infection rate $\lambda$ on a random graph on $n$ vertices with power law degree distributions, mean field calculations suggest that the critical value $\lambda_c$ of the infection rate is positive if…