Stochastic epidemic dynamics on extremely heterogeneous networks

TL;DR

This paper develops a two-dimensional diffusion model to accurately describe the stochastic SIR epidemic dynamics on highly heterogeneous contact networks, capturing the full temporal behavior in large populations.

Contribution

It introduces a novel low-dimensional diffusion approximation for stochastic epidemic models on complex networks with high degree heterogeneity.

Findings

The model accurately approximates the full stochastic dynamics.

Effective for large populations with significant degree heterogeneity.

Remains accurate even when time-scale separation is limited.

Abstract

Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.