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.

• Received 4 December 2001

DOI:https://doi.org/10.1103/PhysRevE.66.016128

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Physical Review E 25th Anniversary Milestones

The year 2018 marks the 25th anniversary of Physical Review E. To celebrate the journal’s rich legacy, during the upcoming year we highlight a series of papers that made important contributions to their field. These milestone articles were nominated by members of the Editorial Board of Physical Review E, in collaboration with the journal’s editors. The 25 milestone articles, including an article for each calendar year from 1993 through 2017 and spanning all major subject areas of the journal, will be unveiled in chronological order and will be featured on the journal website.