Spread of epidemic disease on networks

TLDR

Social network disease spread has attracted recent physics community attention. The paper demonstrates that many SIR models can be solved exactly on diverse networks. They solve SIR models on networks with nonuniform, correlated infection times and probabilities, and also analyze a simple sexually transmitted disease model in a bipartite population. Numerical simulations confirm the exact solutions for SIR epidemics on networks.

Abstract

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.