A unified prediction of computer virus spread in connected networks. (English) Zbl 0995.68007

Summary: We derive two models of viral epidemiology on connected networks and compare results to simulations. The differential equation model easily predicts the expected long term behavior by defining a boundary between survival and extinction regions. The discrete Markov model captures the short term behavior dependent on initial conditions, providing extinction probabilities and the fluctuations around the expected behavior. These analysis techniques provide new insight on the persistence of computer viruses and what strategies should be devised for their control.


68M15 Reliability, testing and fault tolerance of networks and computer systems
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[1] Callaway, D.; Newman, M.; Strogatz, S.; Watts, D., Phys. rev. lett., 85, 5468, (2000)
[2] Newman, M.; Watts, D., Phys. rev. E, 60, 7332, (1999)
[3] Barabasi, A.; Albert, R.; Jeong, H., Physica A, 272, 173, (1999)
[4] Pandit, S.; Amritkar, R., Phys. rev. E, 60, R1119, (1999)
[5] Cohen, R.; Erez, K.; Ben-Avraham, D.; Havlin, S., Phys. rev. lett., 85, 4626, (2000)
[6] Moore, C.; Newman, M., Phys. rev. E, 61, 5678, (2000)
[7] Watts, D.; Strogatz, S., Nature, 393, 440, (1998)
[8] Soh, B.; Dillon, T.; County, P., Comput. networks ISDN syst., 27, 1447, (1995)
[9] Schwartz, I., J. math. biol., 30, 473, (1992)
[10] Kephart, J.; White, S., (), 343-359
[11] Hoppensteadt, F., Mathematical methods of population biology, (1982), Cambridge University Press Cambridge · Zbl 0481.92016
[12] Bailey, N., The mathematical theory of infectious diseases and its applications, (1975), Oxford University Press New York
[13] Pastor-Satorras, R.; Vespignani, A., Phys. rev. lett., 86, 3200, (2001)
[14] Barabasi, A.-L.; Albert, R.; Jeong, H., Physica A, 281, 69, (2000)
[15] W. Spears, L. Billings, I. Schwartz, Modeling viral epidemiology, Naval Research Laboratory, NRL/MR/6700-01-8537, 2001
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