The Annals of Applied Probability

Thresholds for virus spread on networks

Moez Draief, Ayalvadi Ganesh, and Laurent Massoulié

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 18, Number 2 (2008), 359-378.

Dates
First available in Project Euclid: 20 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1206018191

Digital Object Identifier
doi:10.1214/07-AAP470

Mathematical Reviews number (MathSciNet)
MR2398760

Zentralblatt MATH identifier
1137.60051

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 05C80: Random graphs [See also 60B20]
Secondary: 60J85: Applications of branching processes [See also 92Dxx] 90B15: Network models, stochastic

Keywords
Reed–Frost epidemic random graphs epidemic threshold spectral radius giant component

Citation

Draief, Moez; Ganesh, Ayalvadi; Massoulié, Laurent. Thresholds for virus spread on networks. Ann. Appl. Probab. 18 (2008), no. 2, 359--378. doi:10.1214/07-AAP470. https://projecteuclid.org/euclid.aoap/1206018191


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