Simulated identification of epidemic threshold on finite-size networks

TL;DR

This paper investigates methods to accurately identify epidemic thresholds in finite-size networks using simulations and theoretical models, highlighting the effectiveness of variability analysis and the conditions where different mean-field theories perform best.

Contribution

It demonstrates that epidemic variability peaks can reliably determine thresholds and compares the accuracy of HMF and QMF theories against simulations for different network types.

Findings

Variability measure accurately identifies thresholds for SIS and SIR models.

HMF theory predictions align well with simulations except in disassortative networks.

QMF theory provides better estimates in disassortative network cases.

Abstract

Epidemic threshold is one of the most important features of the epidemic dynamics. Through a lot of numerical simulations in classic Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Susceptible (SIS) models on various types of networks, we study the simulated identification of epidemic thresholds on finite-size networks. We confirm that the susceptibility measure goes awry for the SIR model due to the bimodal distribution of outbreak sizes near the critical point, while the simulated thresholds of the SIS and SIR models can be accurately determined by analyzing the peak of the epidemic variability. We further verify the accuracy of theoretical predictions derived by the heterogeneous mean-field theory (HMF) and the quenched mean-field theory (QMF), by comparing them with the simulated threshold of the SIR model obtained from the variability measure. The results show that the HMF prediction agrees very well with the simulated threshold, except the case that the networks are disassortive, in which the QMF prediction is more close to the simulated threshold.