Synergistic epidemic spreading in correlated networks

TL;DR

This paper explores how degree correlation affects epidemic spreading in networks with nonlinear transmission effects, revealing discontinuous transitions and the impact of correlation on epidemic thresholds.

Contribution

It introduces a mean-field model for synergistic SIS epidemics on correlated networks and validates it with approximate master equations and simulations.

Findings

Discontinuous epidemic transitions occur regardless of degree correlation strength.

Positive degree correlation lowers the epidemic threshold, negative raises it.

Approximate master equations agree with mean-field predictions and simulations.

Abstract

We investigate the effect of degree correlation on a susceptible-infected-susceptible (SIS) model with a nonlinear cooperative effect (synergy) in infectious transmissions. In a mean-field treatment of the synergistic SIS model on a bimodal network with tunable degree correlation, we identify a discontinuous transition that is independent of the degree correlation strength unless the synergy is absent or extremely weak. Regardless of synergy (absent or present), a positive and negative degree correlation in the model reduces and raises the epidemic threshold, respectively. For networks with a strongly positive degree correlation, the mean-field treatment predicts the emergence of two discontinuous jumps in the steady-state infected density. To test the mean-field treatment, we provide approximate master equations of the present model. We quantitatively confirm that the approximate master equations agree with not only all qualitative predictions of the mean-field treatment but also corresponding Monte-Carlo simulations.