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Zbl 1137.60051
Draief, Moez; Ganesh, Ayalvadi; Massoulié, Laurent
Thresholds for virus spread on networks. (English)
[J] Ann. Appl. Probab. 18, No. 2, 359-378 (2008). ISSN 1050-5164

Summary: 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-susceptible, infected or removed (cured and no longer susceptible to infection). We characterize how the size of the population that eventually becomes infected depends on the network topology. Specifically, we show that if the ratio of cure to infection rates is larger than the spectral radius of the graph, and the initial infected population is small, then the final infected population is also small in a sense that can be made precise. Conversely, if this ratio is smaller than the spectral radius, then we show in some graph models of practical interest (including power law random graphs) that the average size of the final infected population is large. These results yield insights into what the critical parameters are in determining virus spread in networks.

MSC 2000:: *60K35 Interacting random processes
05C80 Random graphs
60J85 Appl. of branching processes
90B15 Flows in networks with stochastic elements

Keywords: reed-frost epidemic; random graphs; epidemic threshold; spectral radius; giant component

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