The role of bridge nodes between layers on epidemic spreading

Real networks, like the international airport network and the Internet, are composed of interconnected layers (or communities) through a small fraction of nodes that we call here ‘bridge nodes’. These nodes are crucial in the spreading of epidemics because they enable the spread the disease to the entire system. In this workwe study the effect of the bridge nodes on the susceptibleinfected-recoveredmodel in a two layer networkwith a small fraction r of these nodes. In the dynamical process, we theoretically determine that at criticality and for the limit r→0, the time tb at which thefirst bridge node is infected diverges as a power-lawwith r, while above criticality, it appears a crossover between a logarithmic and a power-law behavior. Additionally, in the steady state at criticality, the fraction of recovered nodes scales with r as a power-lawwhose exponent can be understood from the finite size cluster distribution at criticality.We also test ourmodel on the real international airline network and show that ‘high-degree bridge nodes’ reduce the time tb.

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