Related papers: Renewal contact process with dormancy
We study the contact process on the complete graph on $n$ vertices where the rate at which the infection travels along the edge connecting vertices $i$ and $j$ is equal to $ \lambda w_i w_j / n$ for some $\lambda >0$, where $w_i$ are i.i.d.…
Across the tree of life, populations have evolved the capacity to contend with suboptimal conditions by engaging in dormancy, whereby individuals enter a reversible state of reduced metabolic activity. The resulting seed banks are complex,…
Certain renewal theorems are extended to the case that the rate of the renewal process goes to 0 and, more generally, to the case that the drift of the random walk goes to infinity. These extensions are motivated by and applied to the…
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…
We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge…
We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models. Under the assumption that the infection rate is above the critical value for the process on the…
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…
We investigate the contact process on four different types of scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where each potential edge is updated with a rate depending on the strength of the adjacent…
In the present article, we investigate the effects of dormancy on an abstract population genetic level. We first provide a short review of seed bank models in population genetics, and the role of dormancy for the interplay of evolutionary…
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 goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
We consider the contact process with infection rate $\lambda$ on a random $(d+1)$-regular graph with $n$ vertices, $G_n$. We study the extinction time $\tau_{G_n}$ (that is, the random amount of time until the infection disappears) as $n$…
We show existence of a non-trivial phase transition for the contact process, a simple model for infection without immunity, on a network which reacts dynamically to the infection trying to prevent an epidemic. This network initially has the…
We analyze variants of the contact process that are built by modifying the percolative structure given by the graphical construction and develop a robust renormalization argument for proving extinction in such models. With this method, we…
We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of…
The long-time dynamics of the 1D contact process suddenly brought out of an uncorrelated initial state is studied through a light-cone transfer-matrix renormalisation group approach. At criticality, the system undergoes ageing which is…
The symptoms of many infectious diseases influence their host to withdraw from social activity limiting their own potential to spread. Successful transmission therefore requires the onset of infectiousness to coincide with a time when its…
The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection eventually dies out. For larger lambda the…
The factors contributing to the persistence and stability of life are fundamental for understanding complex living systems. Organisms are commonly challenged by harsh and fluctuating environments that are suboptimal for growth and…
We introduce a method to prove metastability of the contact process on Erd\H{o}s-R\'enyi graphs and on configuration model graphs. The method relies on uniformly bounding the total infection rate from below, over all sets with a fixed…