Exact solutions of epidemic models on networks

Details Exact solutions of epidemic models on networks Exact solutions of epidemic models on networks

2002-01-24

arxiv.org/abs/cond-mat/0201433v1

Physics

Condensed Matter

Statistical Mechanics

11 pages, 1 figure

Scientific paper

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 models, and many of their generalizations, can be solved exactly on a wide variety of networks. Solutions are possible for cases with heterogeneous or correlated probabilities of transmission, cases incorporating vaccination, and cases in which the network has complex structure of various kinds. We confirm the correctness of our solutions by comparison with computer simulations of epidemics propagating on the corresponding networks.

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