Related papers: The contact process with semi-infected state on th…
We study how the spread of computer viruses, worms, and other self-replicating malware is affected by the logical topology of the network over which they propagate. We consider a model in which each host can be in one of 3 possible states -…
The critical properties of a cellular automaton model describing the spreading of infection of the Herpes Simplex Virus in corneal tissue are investigated through the dynamic Monte Carlo method. The model takes into account different cell…
We study the spread of multi-competitive viruses over a (possibly) time-varying network of individuals accounting for the presence of shared infrastructure networks that further enables transmission of the virus. We establish a sufficient…
In this paper, we consider the threshold-one contact process and the threshold-one voter model w/o spontaneous death on homogeneous trees $\mathbb{T}_d$, $d\ge 2$. Mainly inspired by the corresponding arguments for ordinary contact…
We consider a quantum walk with two marked vertices, sender and receiver, and analyze its application to perfect state transfer on complete bipartite graphs. First, the situation with both the sender and the receiver vertex in the same part…
Our $N$-intertwined model (now called NIMFA) for virus spread in any network with $N$ nodes is extended to a full heterogeneous setting. The metastable steady-state nodal infection probabilities are specified in terms of a generalized…
We present results on phase transitions of local and global survival in a two-species model on Gilbert graphs. At initial time there is an infection at the origin that propagates on the Gilbert graph according to a continuous-time…
We couple a multi-type stochastic epidemic process with a directed random graph, where edges have random lengths. This random graph representation is used to characterise the fractions of individuals infected by the different types of…
We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the tree vertex degree tends to infinity. We obtain the…
We investigate saturation effects in susceptible-infected-susceptible (SIS) models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity…
Semi-random processes involve an adaptive decision-maker, whose goal is to achieve some predetermined objective in an online randomized environment. They have algorithmic implications in various areas of computer science, as well as…
In this work we investigate a bootstrap percolation process on random graphs generated by a random graph model which combines preferential attachment and edge insertion between previously existing vertices. The probabilities of adding…
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…
It is a longstanding debate on the absence of threshold for susceptible-infected-susceptible (SIS) model on networks with finite second order moment of degree distribution. The eigenvector localization of the adjacency matrix for a network…
We consider a random walk on top of the contact process on $\mathbb{Z}^d$ with $d\geq 1$. In particular, we focus on the "contact process as seen from the random walk". Under the assumption that the infection rate of the contact process is…
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…
Majority bootstrap percolation on a graph $G$ is an epidemic process defined in the following manner. Firstly, an initially infected set of vertices is selected. Then step by step the vertices that have more infected than non-infected…
We numerically study the phase diagram of a three-state host-parasite model on the square lattice motivated by population biology. The model is an extension of the contact process, and the three states correspond to an empty site, a host,…
In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on…
In this work, we analyze a sequential game played in a graph called the Multilevel Critical Node problem (MCN). A defender and an attacker are the players of this game. The defender starts by preventively interdicting vertices (vaccination)…