Related papers: On the growth of one-dimensional reverse immunizat…
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…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
The one-dimensional contact process with weak to intermediate quenched disorder in its transmission rates is investigated via quasi-stationary Monte Carlo simulation. We address the contested questions of both the nature of dynamical…
Contact defects are time-periodic patterns in one space dimension that resemble spatially homogeneous oscillations with an embedded defect in their core region. For theoretical and numerical purposes, it is important to understand whether…
We add a rejection mechanism (negative influence) into a two-dimensions bounded confidence model. The principle is that one shifts aways from a close attitude of one's interlocutor, when there is a strong disagreement on the other attitude.…
We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of $\lambda(l)-\lambda(\infty) = A l^{-s}$, $l$ being the distance from the surface. We concentrate…
We consider Bernoulli bond percolation on a large scale-free tree in the supercritical regime, meaning informally that there exists a giant cluster with high probability. We obtain a weak limit theorem for the sizes of the next largest…
The purpose of this paper is to investigate the long time behaviour for a self-interacting diffusion and a self-interacting velocity jump process. While the diffusion case has already been studied for some particular potential function, the…
Based on a recent model of evolving viruses competing with an adapting immune system [1], we study the conditions under which a viral quasispecies can maximize its growth rate. The range of mutation rates that allows viruses to thrive is…
Contact tracing has been extensively studied from different perspectives in recent years. However, there is no clear indication of why this intervention has proven effective in some epidemics (SARS) and mostly ineffective in some others…
Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the…
In a collection of particles performing independent random walks on $\mathbb Z^d$ we study the spread of an infection with SIR dynamics. Susceptible particles become infected when they meet an infected particle. Infected particles heal and…
The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and…
We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are…
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 consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations…
We consider the super-critical contact process on $\mathbb{Z}^d$. It is known that measures which dominate the upper invariant measure $\mu$ converge exponentially fast to $\mu$. However, the same is not true for measures which are below…
We continue the study of renewal contact processes initiated in a companion paper, where we showed that if the tail of the interarrival distribution $\mu$ is heavier than $t^{-\alpha}$ for some $\alpha <1$ (plus auxiliary regularity…
The spread of infectious disease is strongly influenced by social dynamics. In addition to infection risk, individuals vaccination decisions depend on prevailing social behavior: high infection levels and widespread vaccination can increase…
I study the absorbing-state phase transition in the one-dimensional contact process with mobile disorder. In this model the dilution sites, though permanently inactive, diffuse freely, exchanging positions with the other sites, which host a…