Related papers: On the growth of one-dimensional reverse immunizat…
We consider a supercritical branching process and define a contact tracing mechanism on its genealogical tree. We calculate the growth rate of the post tracing process, and give conditions under which the tracing is strong enough to drive…
We study the supercritical contact process on Galton-Watson trees and periodic trees. We prove that if the contact process survives weakly then it dominates a supercritical Crump-Mode-Jagers branching process. Hence the number of infected…
We consider a L\'evy process that starts from $x<0$ and conditioned on having a positive maximum. When Cram\'er's condition holds, we provide two weak limit theorems as $x\to -\infty$ for the law of the (two-sided) path shifted at the first…
In this paper we study a one-parameter family of attractive reversible nearest particle system on a finite interval. As the length of the interval increases, the time that the nearest particle system first hits the empty set increases in…
The epidemic process on a graph is considered for which infectious contacts occur at rate which depends on whether a susceptible is infected for the first time or not. We show that the Vasershtein coupling extends if and only if secondary…
We are interested in the spread of an epidemic between two communities that have higher connectivity within than between them. We model the two communities as independent Erdos-Renyi random graphs, each with n vertices and edge probability…
We have investigated the effect of the initial condition on the spreading exponents of the one-dimensional pair contact process (PCP) and threshold transfer process (TTP).The non-order field was found to exhibit critical fluctuations,…
We consider a general class of contact processes on $\mathbb{Z}^d$ with potentially long-range interactions. By adapting well established renormalization arguments to the long-range setting we extend by now classical results for…
The extinction transition in the presence of a localized quenched defect is studied numerically. When the bulk is at criticality, the correlation length diverges and even an infinite system cannot "decouple" from the defect. The results…
We analyze infection spreading processes in a system where only a fraction $p$ of individuals can be affected by disease, while remaining $1-p$ individuals are immune. Such a picture can emerge as a natural consequence of previously…
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…
The renewal contact process, introduced in $2019$ by Fontes, Marchetti, Mountford, and Vares, extends the Harris contact process in $\mathbb{Z}^d$ by allowing the possible cure times to be determined according to independent renewal…
The possibility of immunized and improving the entanglement of accelerated systems via local filtering is discussed. The maximum bounds of entanglement depend on the dimensions of the accelerated and the filtered subsystems. If the small…
This paper studies contact processes on general countable groups. It is shown that any such contact process has a well-defined exponential growth rate, and this quantity is used to study the process. In particular, it is proved that on any…
The mobility patterns of individuals in China during the early outbreak of the COVID-19 pandemic exhibit reversible changes -- in many regions, the mobility first decreased significantly and later restored. Based on this observation, here…
The aim of this paper is to study two models for a bacterial population subject to antibiotic treatments. It is known that some bacteria are sensitive to antibiotics. These bacteria are in a state called persistence and each bacterium can…
In this paper we are concerned with contact processes on open clusters of oriented percolation in $Z^d$, where the disease spreads along the direction of open edges. We show that the two critical infection rates in the quenched and annealed…
We study the contact process on random graphs with low infection rate $\lambda$. For random $d$-regular graphs, it is known that the survival time is $O(\log n)$ below the critical $\lambda_c$. By contrast, on the Erd\H{o}s-R\'enyi random…
In this paper we are concerned with contact processes with random vertex weights on oriented lattices. In our model, we assume that each vertex x of Z^d takes i. i. d. positive random value \rho(x). Vertex y infects vertex x at rate…
We study the dynamics of secondary infections on networks, in which only the individuals currently carrying a certain primary infection are susceptible to the secondary infection. In the limit of large sparse networks, the model is mapped…