Role of bridge nodes in epidemic spreading: Different regimes and crossovers

TL;DR

This paper analyzes how bridge nodes influence epidemic spreading in interconnected communities, revealing different power-law behaviors and crossover points that inform epidemic control strategies.

Contribution

It provides a theoretical framework for understanding the role of bridge nodes in epidemic dynamics across interconnected networks, including power-law behaviors and crossover phenomena.

Findings

Power-law asymptotic behaviors of recovered fraction as bridge node fraction approaches zero.

Identification of crossover points with different power-law regimes.

Mechanistic explanation of how finite clusters connect into the giant component.

Abstract

Power-law behaviors are common in many disciplines, especially in network science. Real-world networks, like disease spreading among people, are more likely to be interconnected communities, and show richer power-law behaviors than isolated networks. In this paper, we look at the system of two communities which are connected by bridge links between a fraction $r$ of bridge nodes, and study the effect of bridge nodes to the final state of the Susceptible-Infected-Recovered model, by mapping it to link percolation. By keeping a fixed average connectivity, but allowing different transmissibilities along internal and bridge links, we theoretically derive different power-law asymptotic behaviors of the total fraction of the recovered $R$ in the final state as $r$ goes to zero, for different combinations of internal and bridge link transmissibilities. We also find crossover points where $R$ follows different power-law behaviors with $r$ on both sides when the internal transmissibility is below but close to its critical value, for different bridge link transmissibilities. All of these power-law behaviors can be explained through different mechanisms of how finite clusters in each community are connected into the giant component of the whole system, and enable us to pick effective epidemic strategies and to better predict their impacts.