Related papers: Some rigorous results for the stacked contact proc…
We study the limiting behavior of an interacting particle system evolving on the lattice $Z^{d}$ for $d\ge 3$. The model is known as the contact process with rapid stirring. The process starts with a single particle at the origin. Each…
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…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
We consider a non-attractive three state contact process on $\mathbb Z$ and prove that there exists a regime of survival as well as a regime of extinction. In more detail, the process can be regarded as an infection process in a dynamic…
We introduce a model of epidemics among moving particles on any locally finite graph. At any time, each vertex is empty, occupied by a healthy particle, or occupied by an infected particle. Infected particles recover at rate $1$ and…
We study the contact process in the regime of small infection rates on finite scale-free networks with stationary dynamics based on simultaneous updating of all connections of a vertex. We allow the update rates of individual vertices to…
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…
We investigate the time evolution and stationary states of a stochastic, spatially discrete, population model (contact process) with spatial heterogeneity and imposed drift (wind) in one- and two-dimensions. We consider in particular a…
Contact tracing can be thought of as a race between two processes: an infection process and a tracing process. In this paper, we study a simple model of infection spreading on a tree, and a tracer who stabilizes one node at a time. We focus…
We consider a Spatial Markov Chain model for the spread of viruses. The model is based on the principle to represent a graph connecting nodes, which represent humans. The vertices between the nodes represent relations between humans. In…
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…
The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth…
We describe a stochastic birth-and-death model of evolution of horizontally transferred genes in microbial populations. The model is a generalization of the stochastic model described by Berg and Kurland and includes five parameters: the…
Motivated by the study of social insects, we introduce a stochastic model based on interacting particle systems in order to understand the effect of communication on the division of labor. Members of the colony are located on the vertex set…
We introduce a general class of branching Markov processes for the modelling of a parasite infection in a cell population. Each cell contains a quantity of parasites which evolves as a diffusion with positive jumps. The drift, diffusive…
The contact process is a simple infection spreading model showcasing an out-of-equilibrium phase transition between a macroscopically active and an inactive phase. Such absorbing state phase transitions are often sensitive to the presence…
We model hypothetical bio-dispersal within a single Galactic region using the stochastic infection dynamics process, which is inspired by these local properties of life dispersal on Earth. We split the population of stellar systems into…
Contacts between individuals serve as pathways where infections may propagate. These contact patterns can be represented by network structures. Static structures have been the common modeling paradigm but recent results suggest that…
We consider a stochastic model, describing the growth of two competing infections on $\mathbb{R}^d$. The growth takes place by way of spherical outbursts in the infected region, an outburst in the type 1 (2) infected region causing all…