Bifurcations in synergistic epidemics on random regular graphs

TL;DR

This paper analyzes how synergy influences epidemic spreading on random regular graphs, revealing complex bifurcation behaviors and contrasting effects with non-synergistic models through analytical and numerical methods.

Contribution

It provides the first detailed analysis of bifurcations in synergistic epidemics on random regular graphs, highlighting the impact of cooperation on epidemic dynamics.

Findings

Identification of three regimes: non-active, active, and bi-stable.

Bifurcation diagrams depend on node degree.

Synergy causes effects contrasting with non-synergistic epidemics.

Abstract

The role of cooperative effects (i.e. synergy) in transmission of infection is investigated analytically and numerically for epidemics following the rules of Susceptible-Infected-Susceptible (SIS) model defined on random regular graphs. Non-linear dynamics are shown to lead to bifurcation diagrams for such spreading phenomena exhibiting three distinct regimes: non-active, active and bi-stable. The dependence of bifurcation loci on node degree is studied and interesting effects are found that contrast with the behaviour expected for non-synergistic epidemics.