Related papers: On an epidemic model on finite graphs
We propose an epidemic compartment model, which includes mortality caused by the disease, but excludes demographic birth and death processes. Individuals are represented by random walkers, which are in one of the following states…
Metapopulation models have been a powerful tool for both theorizing and simulating epidemic dynamics. In a metapopulation model, one considers a network composed of subpopulations and their pairwise connections, and individuals are assumed…
Let $(G,\mu)$ be a uniformly elliptic random conductance graph on $\mathbb{Z}^d$ with a Poisson point process of particles at time $t=0$ that perform independent simple random walks. We show that inside a cube $Q_K$ of side length $K$, if…
We discuss various models for epidemics on networks that rely on Markov chains. Random walks on graphs are often used to predict epidemic spread and to investigate possible control actions to mitigate them. In this study, we demonstrate…
Consider $N$ particles performing random walks on the $\epsilon$-grid $(\epsilon Z)^d$, $\epsilon>0$ with branching and density-dependent selection: When one of the particles branches, a particle is removed from the most populated site. The…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
We present analytical results for the distribution of cover times of random walks (RWs) on random regular graphs consisting of $N$ nodes of degree $c$ ($c \ge 3$). Starting from a random initial node at time $t=1$, at each time step $t \ge…
The aim of this work is to demonstrate that the continuous-time frog model can spread arbitrary fast. The set of sites visited by an active particle can become infinite in a finite time.
We investigate the quantum dynamics of particles on graphs ("quantum random walks"), with the aim of developing quantum algorithms for determining if two graphs are isomorphic (related to each other by a relabeling of vertices). We focus on…
The contact process, or SIS epidemic, is a continuous-time Markov process used to model the spread of infection on a graph. Each vertex is either healthy or infected, and each infected vertex independently infects each of its healthy…
The bootstrap percolation (or threshold model) is a dynamic process modelling the propagation of an epidemic on a graph, where inactive vertices become active if their number of active neighbours reach some threshold. We study an…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
Self-activation coupled to a transport mechanism results in traveling waves that describe polymerization reactions, forest fires, tumor growth, and even the spread of epidemics. Diffusion is a simple and commonly used model of particle…
We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the compartments susceptible (S); incubated - infected yet…
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…
We study the annihilating random walk with long-range interaction in one dimension. Each particle performs random walks on a one-dimensional ring in such a way that the probability of hopping toward the nearest particle is $W= [1 - \epsilon…
We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…
Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the…
We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on $\mathbb{R}^d$. This class includes the age-dependent random connection model and the soft Boolean…