Related papers: Renewal contact process with dormancy
We consider an interacting particle system on $\Z^d$ with finite state space and interactions of infinite range in a high-noise regime. Assuming that the rate of change is continuous and that a Dobrushin-like condition holds, we show that…
In this article, we introduce a contact process with aging: in this generalization of the classical contact process, each particle has an integer age that influences its ability to give birth. We prove here a shape theorem for this process…
The regular tree corresponds to the random regular graph as its local limit. For this reason the famous double phase transition of the contact process on regular tree has been seen to correspond to a phase transition on the large random…
Renewal process is a point process where an inter-event time between successive renewals is an independent and identically distributed random variable. Alternating renewal process is a dichotomous process and a slight generalization of the…
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 occupy any…
A new, conceptual proof approach for establishing the existence of regenerative space-time points for symmetric, translation invariant, finite-range interaction contact processes on survival is shown. The proof is elementary, complements…
In this paper, we introduce a type switching mechanism for the Contact Process on the lattice $\mathbb{Z}^d$. That is, we allow the individual particles/sites to switch between two (or more) types independently of one another, and the…
The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where infected (1) individuals infect susceptible (0) neighbors at rate $\lambda$ and infected individuals recover ($1 \longrightarrow 0$)…
If the step distribution in a renewal process has finite mean and regularly varying tail with index -{\alpha}, 1<{\alpha}<2, the first two terms in the asymptotic expansion of the renewal function have been known for many years. Here we…
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…
A proof is provided of a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof is based on a coupling argument that traces the…
Dormancy is a widespread adaptive strategy that enables populations to persist in fluctuating environments, yet how its benefits depend on the temporal structure of environmental variability remains unclear. We examine how dormancy…
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…
This study examines the interface of three elements during co-contagion diffusion: the \textbf{synergy} between contagions, the \textbf{dormancy} rate of each individual contagion, and the \textbf{multiplex network topology}. Dormancy is…
We consider a spatial stochastic model for a pathogen population growing inside a host that attempts to eliminate the pathogens through its immune system. The pathogen population is divided into different types. A pathogen can either…
Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with $N$ dormant individuals waking up independently of each other according to a given distribution. Once an individual…
We replicate a renewal process at random times, which is equivalent to nesting two renewal processes, or considering a renewal process subject to stochastic resetting. We investigate the consequences on the statistical properties of the…
In the last decade Hawkes processes have received much attention as models for functional connectivity in neural spiking networks and other dynamical systems with a cascade behavior. In this paper we establish a renewal approach for…
We investigate a stochastic individual-based model for the population dynamics of host-virus systems where the microbial hosts may transition into a dormant state upon contact with virions, thus evading infection. Such a contact-mediated…
This paper is concerned with contact process with random vertex weights on regular trees, and study the asymptotic behavior of the critical infection rate as the degree of the trees increasing to infinity. In this model, the infection…