Dynamics of Stochastic Epidemics on Heterogeneous Networks

TL;DR

This paper develops a stochastic SIR epidemic model on heterogeneous networks, revealing how the network's degree distribution moments influence epidemic variability, especially during early exponential growth.

Contribution

It introduces a diffusion limit model for stochastic epidemics on heterogeneous networks, highlighting the role of higher order degree moments in epidemic variability.

Findings

The first three moments of the degree distribution determine the variance in disease prevalence.

Skewness of the degree distribution affects epidemic variability.

Model predictions closely match simulations for city-sized populations.

Abstract

Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a heterogeneous network. Using this, we consider analytically the early asymptotic exponential growth phase of such epidemics, showing how the higher order moments of the network degree distribution enter into the stochastic behaviour of the epidemic. We find that the first three moments of the network degree distribution are needed to specify the variance in disease prevalence fully, meaning that the skewness of the degree distribution affects the variance of the prevalence of infection. We compare these asymptotic results to simulation and find a close agreement for city-sized populations.