Related papers: A model for infection on graphs
The history of infections and epidemics holds famous examples where understanding, containing and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV and most computer viruses, spread person to…
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…
Contacts between individuals serve as pathways where infections may propagate. These contact patterns can be represented by network structures. Static structures have been the common modeling paradigm but recent results suggest that…
In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission…
The manner epidemics occurs in a social network depends on various elements, with two of the most influential being the relationships among individuals in the population and the mechanism of transmission. In this paper, we assume that the…
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 discuss various models for epidemics on networks that rely on Markov chains. Random walks on graphs are often used to predict epidemic spread and to investigate possible control actions to mitigate them. In this study, we demonstrate…
Infectious disease remains, despite centuries of work to control and mitigate its effects, a major problem facing humanity. This paper reviews the mathematical modelling of infectious disease epidemics on networks, starting from the…
A problem closely related to epidemiology, where a subgraph of 'infected' links is defined inside a larger network, is investigated. This subgraph is generated from the underlying network by a random variable, which decides whether a link…
Random walk is one of the basic mechanisms found in many network applications. We study the epidemic spreading dynamics driven by biased random walks on complex networks. In our epidemic model, each time infected nodes constantly spread…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
We study numerically the variability of the outbreak of diseases on complex networks. We use a SI model to simulate the disease spreading at short times, in homogeneous and in scale-free networks. In both cases, we study the effect of…
Researchers, policy makers, and engineers need to make sense of data from spreading processes as diverse as rumor spreading in social networks, viral infections, and water contamination. Classical questions include predicting infection…
The spread of an infectious disease can, in some cases, promote the propagation of other pathogens favouring violent outbreaks, which cause a discontinuous transition to an endemic state. The topology of the contact network plays a crucial…
In this paper, we investigate the exact asymptotic behavior of the connectivity probability in the Erdos-Renyi graph G(n,p), under different asymptotic assumptions on the edge probability p=p(n). We propose a novel approach based on the…
The influence of the network's structure on the dynamics of spreading processes has been extensively studied in the last decade. Important results that partially answer this question show a weak connection between the macroscopic behavior…
In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless…
When averages over all starting points are considered, the Type Problem for the recurrence or transience of a simple random walk on an inhomogeneous network in general differs from the usual "local" Type Problem. This difference leads to a…
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 -…
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…