Related papers: Subcritical contact processes seen from a typical …
The existence of a weak survival region is established for the anisotropic symmetric contact process on a homogeneous tree T_{2d} of degree 2d > 2: For parameter values in a certain connected region of positive Lebesgue measure, the…
We study the behaviour of the rightmost occupied site in two models: the Spont process and the contact process with inherited sterility, in dimension 1. Both can be viewed as contact processes evolving in dynamic random environments, where…
The susceptible-exposed-infectious-susceptible (SEIS) model is well-known in mathematical epidemiology as a model of infection in which there is a latent period between the moment of infection and the onset of infectiousness. The…
In this paper we are concerned with the two-stage contact process introduced in \cite{Krone1999} on a high-dimensional lattice. By comparing this process with an auxiliary model which is a linear system, we obtain two limit theorems for…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
A key parameter in models for the spread of infectious diseases is the basic reproduction number $R_0$, which is the expected number of secondary cases a typical infected primary case infects during its infectious period in a large mostly…
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…
The key to our investigation is an improved (and in a sense sharp) understanding of the survival time of the contact process on star graphs. Using these results, we show that for the contact process on Galton-Watson trees, when the…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
We consider the contact process with dormancy, where wake-up times follow a renewal process. Without infection between dormant individuals, we show that the process under certain conditions grows at most logarithmically. On the other hand,…
Capturing the structured mixing within a population is key to the reliable projection of infectious disease dynamics and hence informed control. Both heterogeneity in the number of contacts and age-structured mixing have been repeatedly…
We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
We prove that the supercritical one-dimensional contact process survives in certain wedge-like space-time regions, and that when it survives it couples with the unrestricted contact process started from its upper invariant measure. As an…
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 study a class of individual-based, fixed-population size epidemic models under general assumptions, e.g., heterogeneous contact rates encapsulating changes in behavior and/or enforcement of control measures. We show that the…
We study spreading on networks where the contact dynamics between the nodes is governed by a random process and where the inter-contact time distribution may differ from the exponential. We consider a process of imperfect spreading, where…
The three state contact process is the modification of the contact process at rate $\mu$ in which first infections occur at rate $\lambda$ instead. Chapters 2 and 3 consider the three state contact process on (graphs that have as set of…
The self-similar growth-fragmentation equation describes the evolution of a medium in which particles grow and divide as time proceeds, with the growth and splitting of each particle depending only upon its size. The critical case of the…