Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks

TL;DR

This paper develops an analytical approach combining two theoretical methods to accurately model the dynamic correlations in the SIS epidemic model on networks, improving predictions of disease prevalence and thresholds.

Contribution

It introduces a novel analytical solution for the SIS model on networks by integrating heterogeneous mean-field theory and effective degree methods, accounting for dynamic correlations.

Findings

Derived accurate expressions for epidemic threshold.

Provided precise estimates of disease prevalence.

Generalized approach to other stochastic models.

Abstract

The Susceptible-Infected-Susceptible model is a canonical model for emerging disease outbreaks. Such outbreaks are naturally modeled as taking place on networks. A theoretical challenge in network epidemiology is the dynamic correlations coming from that if one node is occupied, or infected (for disease spreading models), then its neighbors are likely to be occupied. By combining two theoretical approaches---the heterogeneous mean-field theory and the effective degree method---we are able to include these correlations in an analytical solution of the SIS model. We derive accurate expressions for the average prevalence (fraction of infected) and epidemic threshold. We also discuss how to generalize the approach to a larger class of stochastic population models.