DIMACS Center, CoRE Building, Rutgers University

**Organizers:****Lora Billings**, Montclair State University, billingsl@mail.montclair.edu**Stephanie Forrest**, University of New Mexico, forrest@cs.unm.edu**Alun Lloyd**, Institute for Advanced Study, alun@alunlloyd.com**Ira Schwartz**, Naval Research Laboratory, schwartz@nlschaos.nrl.navy.mil

**Co-sponsored by DIMACS, the National Science Foundation (NSF) and the Office of Naval Research (ONR).**

Topics of this working group will be discussed next at the second meeting of the working group on Spatio-temporal and Network Modeling

**This meeting is by invitation only.**

The study of analogies between computer viruses and biological viruses, and associated immune systems, offers promise for the understanding of both and this working group will investigate these analogies. Early studies of computer viruses spreading through a network were based on models of population dynamics (e.g., [Kephart and White (1991)]). Ridley and Baker [Ridley and Baker (1997)] made specific comparisons between the dynamics of replicating agents in prion diseases (such as BSE) and computer viruses. However, there has not been much theoretical work until recently. Of note is the article by Lloyd and May [Lloyd and May (2001)] which supports the view that the methods of TCS, combined in clever new ways with the traditional tools of population biology, might cast light on both computer and natural viruses. There is also the work of Aron et al. [Aron et al. (2002)], who conducted a Computer Virus Epidemiology Survey to develop a simulation model for the spread of computer viruses in workgroups and provide a better understanding of strategies to reduce their impact. Other new popular approaches are "scale-free" and "small world" networks, which study the topology of the network. (See [Barabasi, Albert and Jeong (2000), Pastor-Satorras and Vespignani (2001), Watts (1999), Watts and Strogatz (1998)].) In addition to building on the graph-theoretical approach of [Kephart and White (1991)], we will revisit the original population dynamics approach, to incorporate recent work from biology into models currently being considered for the spread of computer viruses. For example, we will build on the work of Richards, Wilson, and Socolar [Richards, Wilson and Socolar (1999)], who studied the propagation of a lethal disease in a spatially explicit model and found major differences between populations that were sessile and those that were mobile. We will also compare the efficacy of discrete and continuous models, explore the addition of time delays and/or stochastic perturbations ([Aparicio and Solari (2001), Billings and Schwartz (2001)]), and compare the spread mechanisms at the molecular level. As a starting point, our group will seek to identify which biological parameters carry over to models of computer viruses and which need modification. For example, the contact rate is a parameter that captures the effective transmission of a disease. We will use existing data to model this parameter and produce a metric to predict the spread of a computer virus. We will also explore the various architectures used to model computer networks, variations in topology, time dependence, and spatial dependence. The goal will be to model the spread of a computer virus and assess "vaccination" strategies in a robust computer network. The group will involve computer scientists, mathematicians, and epidemiologists who will bring to bear the variety of expertise needed to make progress on this problem.

Barabasi, A.-L., Albert, R., and Jeong, H. (2000),
"Scale-free characteristics of random networks: The topology of the world-wide web,"
*Physica A*, **281**, 69.

Billings, L., and Schwartz, I. (2002),
"Exciting chaos with noise: unexpected dynamics in epidemic outbreaks,"
*J. Math. Biology*, **44**, 31-48.

http://www.csam.montclair.edu/%7Ebillings/research/research.html

Kephart, J., and White, S. (1991),
"Directed-graph epidemiological models of computer viruses,"
in *Proc. of the 1991 Computer Society Symposium on Research in Security and Privacy*, 343-359.

Lloyd, A.L., and May, R.M. (2001), "How viruses spread among computers and people,"
*Science*, **292**, 1316-1317.

Pastor-Satorras, R., and Vespignani, A. (2001),
"Epidemic spreading in scale-free networks,"
*Phys. Rev. Lett.*, **86**, 3200.

Richards, S., Wilson, W., and Socolar, J. (1999),
"Selection for intermediate mortality and reproduction rates in a spatially structured population,"
*Proc. R. Soc. London*, **266**, 2383.

Ridley, R., and Baker, H. (1997),
"The nature of transmission in prion diseases,"
*Neuropathology and Appl. Neurobiology*, **23**, 273.

Watts, D.J. (1999), *Small Worlds: The Dynamics of Networks between Order and Randomness*,
Princeton University Press, Princeton, NJ.

Watts, D.J., and Strogatz, S.H. (1998),
"Collective dynamics of 'small-world' networks,"
*Nature*, **393**, 440-442.

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Document last modified on May 31, 2002.