Related papers: Renewal contact process with dormancy
After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because…
Cell movement and intercellular signaling occur simultaneously during the development of tissues, but little is known about how movement affects signaling. Previous theoretical studies have shown that faster moving cells favor…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
The aim of this paper is to underline the relation between reversible growth processes and invariant percolation. We present two models of interacting branching random walks (BRWs), truncated BRWs and competing BRWs, where survival of the…
Due to wide applications in diverse fields, random walks subject to stochastic resetting have attracted considerable attention in the last decade. In this paper, we study discrete-time random walks on complex network with multiple resetting…
Bezuidenhout and Grimmett proved that the critical contact process dies out. Here, we generalize the result to the so called contact process in a random evolving environment (CPREE), introduced by Erik Broman. This process is a…
In this paper we introduce a contact process in an evolving random environment (CPERE) on a connected and transitive graph with bounded degree, where we assume that this environment is described through an ergodic spin systems with finite…
Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the…
Renewal theorems are developed for point processes with interarrival times $W_n=\xi(X_{n+1}X_n\cdots)$, where $(X_n)_{n\in\mathbb Z}$ is a stochastic process with finite state space $\Sigma$ and $\xi\colon\Sigma_A\to\mathbb R$ is a H\"older…
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…
Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same…
We review the theory of renewal reward processes, which describes renewal processes that have some cost or reward associated with each cycle. We present a new simplified proof of the renewal reward theorem that mimics the proof of the…
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…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
Unlike most other laws of nature, the second law of thermodynamics is of a statistical nature, according to Boltzmann, meaning that its reliability arises from the vast number of particles present in macroscopic systems. This means that…
We live within an increasingly technological, information-laden environment for the first time in human evolution.This subjects us, and will continue to subject us in an accelerating fashion, to an unremitting exposure to meaningful…
We investigate the one-dimensional telegraph random process in the presence of an elastic boundary at the origin. This process describes a finite-velocity random motion that alternates between two possible directions of motion (positive or…
There are two contrasting explanations of sleep: as a proximate, essential physiological function or as an adaptive state of inactivity and these hypotheses remain widely debated. To investigate the adaptive significance of sleep, we…
We derive conditions under which alternating renewal processes can be used to construct correlated Poisson processes. The pairwise correlation function is also derived, showing that the resulting correlations can be negative. The technique…
This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…