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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 -…
In the real world, many complex systems interact with other systems. In addition, the intra- or inter-systems for the spread of information about infectious diseases and the transmission of infectious diseases are often not random, but with…
In a networked system, functionality can be seriously endangered when nodes are infected, due to internal random failures or a contagious virus that develops into an epidemic. Given a snapshot of the network representing the nodes' states…
This paper develops and analyzes optimization models for rapid detection of viruses in large contact networks. In the model, a virus spreads in a stochastic manner over an undirected connected graph, under various assumptions on the spread…
This paper deals with the statistical signal pro- cessing over graphs for tracking infection diffusion in social networks. Infection (or Information) diffusion is modeled using the Susceptible-Infected-Susceptible (SIS) model. Mean field…
Given a network represented by a graph $G=(V,E)$, we consider a dynamical process of influence diffusion in $G$ that evolves as follows: Initially only the nodes of a given $S\subseteq V$ are influenced; subsequently, at each round, the set…
Real epidemic spreading networks often composed of several kinds of networks interconnected with each other, and the interrelated networks have the different topologies and epidemic dynamics. Moreover, most human diseases are derived from…
In this paper we consider the problem of transmission across a graph and how to effectively control/restrict it with limited resources. Transmission can represent information transfer across a social network, spread of a malicious virus…
Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
Multigraphs are graphs in which multiple links between pairs of nodes are allowed, whereas they are forbidden in simple graphs, the latter being widely used in network science. Simple graphs generated by the configuration model have served…
Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…
Disease spread in most biological populations requires the proximity of agents. In populations where the individuals have spatial mobility, the contact graph is generated by the "collision dynamics" of the agents, and thus the evolution of…
The spread of influence in social networks is studied in two main categories: the progressive model and the non-progressive model (see e.g. the seminal work of Kempe, Kleinberg, and Tardos in KDD 2003). While the progressive models are…
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three…
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…
A rumor spreading in a social network or a disease propagating in a community can be modeled as an infection spreading in a network. Finding the infection source is a challenging problem, which is made more difficult in many applications…
We study a simple model of epidemics where an infected node transmits the infection to its neighbors independently with probability $p$. This is also known as the independent cascade or Susceptible-Infected-Recovered (SIR) model with fixed…
The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…
We examine how the behaviour of high degree vertices in a network affects whether an infection spreads through communities or jumps between them. We study two stochastic susceptible-infected-recovered (SIR) processes and represent our…