The spread of epidemic disease on networks

TL;DR

This paper provides exact solutions for the spread of epidemic diseases on various networks, including complex and structured populations, extending traditional models to more realistic scenarios.

Contribution

It introduces exact solutions for SIR epidemic models on diverse networks with non-uniform, correlated transmission probabilities and structured populations.

Findings

Exact solutions for SIR models on different networks

Validation through numerical simulations

Extension to structured populations like sexually transmitted diseases

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 non-uniform 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.