Multistage onset of epidemics in heterogeneous networks

TL;DR

This paper presents a new theory for SIS epidemic models on networks that captures multistage epidemic onset and improves prediction accuracy in heterogeneous networks, highlighting the role of hubs in sustaining epidemics.

Contribution

It introduces a comprehensive theory accounting for dynamic correlations and multistage onset in scale-free networks, enhancing understanding of epidemic thresholds and prevalence.

Findings

Identifies multistage epidemic onset with multiple susceptibility peaks.

Shows hubs can sustain epidemics beyond the global threshold.

Improves accuracy of prevalence predictions near the threshold.

Abstract

We develop a theory for the susceptible-infected-susceptible (SIS) epidemic model on networks that incorporate both network structure and dynamic correlations. This theory can account for the multistage onset of the epidemic phase in scale-free networks. This phenomenon is characterized by multiple peaks in the susceptibility as a function of the infection rate. It can be explained by that, even under the global epidemic threshold, a hub can sustain the epidemics for an extended period. Moreover, our approach improves theoretical calculations of prevalence close to the threshold in heterogeneous networks and also can predict the average risk of infection for neighbors of nodes with different degree and state on uncorrelated static networks.