Open Access
April 2008 Thresholds for virus spread on networks
Moez Draief, Ayalvadi Ganesh, Laurent Massoulié
Ann. Appl. Probab. 18(2): 359-378 (April 2008). DOI: 10.1214/07-AAP470


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.


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Moez Draief. Ayalvadi Ganesh. Laurent Massoulié. "Thresholds for virus spread on networks." Ann. Appl. Probab. 18 (2) 359 - 378, April 2008.


Published: April 2008
First available in Project Euclid: 20 March 2008

zbMATH: 1137.60051
MathSciNet: MR2398760
Digital Object Identifier: 10.1214/07-AAP470

Primary: 05C80 , 60K35
Secondary: 60J85 , 90B15

Keywords: epidemic threshold , Giant component , Random graphs , Reed–Frost epidemic , spectral radius

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.18 • No. 2 • April 2008
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