Simulated identification of epidemic threshold on finite-size networks

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 meanfield 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.

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“…Differing from the SIS (Susceptible-Infected-Susceptible) model, it is not an easy thing to determine the epidemic threshold for the SIR model owing to the non-zero value of R. In doing so, in Ref. 28 , Shu et al suggested that the variability measure…”

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“…2(c) later. Note that given the contacting randomness in the CP model [33,34], there is a large fluctuation of Δr R , especially near the critical point [35].…”