Related papers: Infection spread for the frog model on trees
We discuss how spreading processes on temporal networks are impacted by the shape of their inter-event time distributions. Through simple mathematical arguments and toy examples, we find that the key factor is the ordering in which events…
We extend some results of Itai Benjamini and Yuri Lima (see \href{http://arxiv.org/pdf/1305.2610.pdf}{\cite{Benjamini}}). In this paper they consider a binary tree $\mathbb T_n$ of height $n$, each leaf is either infected by one of $k$…
Consider a rooted $N$-ary tree. To every vertex of this tree, we attach an i.i.d. continuous random variable. A vertex is called accessible if along its ancestral line, the attached random variables are increasing. We keep accessible…
Physical contact or proximity is often a necessary condition for the spread of infectious diseases. Common destinations, typically referred to as hubs or points of interest, are arguably the most effective spots for the type of disease…
Spatial models for spread of an epidemic may be mapped onto bond percolation. We point out that with disorder in the strength of contacts between individuals patchiness in the spread of the epidemic is very likely, and the criterion for…
A theory of the spread of epidemics is formulated on the basis of pairwise interactions in a dilute system of random walkers (infected and susceptible animals) moving in n dimensions. The motion of an animal pair is taken to obey a…
Understanding spreading dynamics will benefit society as a whole in better preventing and controlling diseases, as well as facilitating the socially responsible information while depressing destructive rumors. In network-based spreading…
We introduce a model of traveling agents ({\it e.g.} frugivorous animals) who feed on randomly located vegetation patches and disperse their seeds, thus modifying the spatial distribution of resources in the long term. It is assumed that…
We introduce and study the problem of posterior inference on tree-structured graphical models in the presence of a malicious adversary who can corrupt some observed nodes. In the well-studied broadcasting on trees model, corresponding to…
We study degree-penalized contact processes on Galton-Watson trees (GW) and the configuration model. The model we consider is a modification of the usual contact process on a graph. In particular, each vertex can be either infected or…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
We address the question of understanding the effect of the underlying network topology on the spread of a virus and the dissemination of information when users are mobile performing independent random walks on a graph. To this end we…
Global transport and communication networks enable information, ideas and infectious diseases now to spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like…
We study the following microscopic model of infection or epidemic reaction: red and blue particles perform independent nearest-neighbor continuous-time symmetric random walks on the integer lattice $\mathbb{Z}$ with jump rates $D_R$ for red…
We study epidemic arrival times in meta-population disease models through the lens of front propagation into unstable states. We demonstrate that several features of invasion fronts in the PDE context are also relevant to the network case.…
Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the…
We propose a compartmental model for vector-transmitted diseases, such as Malaria and Dengue, spreading over complex networks. Individuals are represented by independent random walkers and vectors by infected nodes. Both walkers and nodes…
We introduce an Ising approach to study the spread of malware. The Ising spins up and down are used to represent two states--online and offline--of the nodes in the network. Malware is allowed to propagate amongst online nodes and the rate…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
In this paper we consider a simple virus infection spread model on a finite population of $n$ agents connected by some neighborhood structure. Given a graph $G$ on $n$ vertices, we begin with some fixed number of initial infected vertices.…