Network localization is unalterable by infections in bursts

TL;DR

This paper investigates a bursty SIS epidemic model on networks, revealing that infection bursts do not alter the localization of disease spread, even as network size grows and eigenvalues diverge.

Contribution

It introduces a bursty SIS model analyzed via mean-field approximation, showing that infection bursts cannot delocalize disease spread on localized networks.

Findings

Maximum near-threshold prevalence tends to zero on localized networks.

Infection bursts do not cause delocalization despite diverging eigenvalues.

Results confirmed on synthetic and real-world networks.

Abstract

To shed light on the disease localization phenomenon, we study a bursty susceptible-infected-susceptible (SIS) model and analyze the model under the mean-field approximation. In the bursty SIS model, the infected nodes infect all their neighbors periodically, and the near-threshold steady-state prevalence is non-constant and maximized by a factor equal to the largest eigenvalue $\lambda_1$ of the adjacency matrix of the network. We show that the maximum near-threshold prevalence of the bursty SIS process on a localized network tends to zero even if $\lambda_1$ diverges in the thermodynamic limit, which indicates that the burst of infection cannot turn a localized spreading into a delocalized spreading. Our result is evaluated both on synthetic and real networks.