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The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection eventually dies out. For larger lambda the…
This paper is a further investigation of the problem studied in \cite{xue2020hydrodynamics}, where the authors proved a law of large numbers for the empirical measure of the weakly asymmetric normalized binary contact path process on…
The binary contact path process (BCPP) introduced in Griffeath (1983) describes the spread of an epidemic on a graph and is an auxiliary model in the study of improving upper bounds of the critical value of the contact process. In this…
We study the following microscopic model of infection or epidemic reaction: red and blue particles perform independent nearest-neighbor continuous-time symmetric random walks on the integer lattice $\mathbb{Z}$ with jump rates $D_R$ for red…
We study the contact process on random graphs with low infection rate $\lambda$. For random $d$-regular graphs, it is known that the survival time is $O(\log n)$ below the critical $\lambda_c$. By contrast, on the Erd\H{o}s-R\'enyi random…
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…
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 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…
We study multi-patch epidemic models where individuals may migrate from one patch to another in either of the susceptible, exposed/latent, infectious and recovered states. We assume that infections occur both locally with a rate that…
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…
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected,…
We study survival and extinction of a long-range infection process on a diluted one-dimensional lattice in discrete time. The infection can spread to distant vertices according to a Pareto distribution, however spreading is also prohibited…
This paper is concerned with a natural variant of the contact process modeling the spread of knowledge on the integer lattice. Each site is characterized by its knowledge, measured by a real number ranging from 0 = ignorant to 1 =…
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…
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 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…
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…
We study a dynamics of the epidemiological infection spreading at different values of the risk factor $\beta$ (a control parameter) with the using of dynamic Monte Carlo approach (DMC). In our toy model, the infection transmits due to…
We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all…
We study degree-penalized contact processes on Galton-Watson trees (GW) and the configuration model. The model we consider is a modification of the usual contact process on a graph. In particular, each vertex can be either infected or…