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Phys. Rev. E 66, 016128 (2002) [11 pages]

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Spread of epidemic disease on networks

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M. E. J. Newman
Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109-1120
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501

Received 4 December 2001; published 26 July 2002

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are nonuniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.

© 2002 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.66.016128
DOI:
10.1103/PhysRevE.66.016128
PACS:
89.75.Hc, 87.23.Ge, 05.70.Fh, 64.60.Ak