Synchronized and mixed outbreaks of coupled recurrent epidemics

TL;DR

This paper investigates how recurrent epidemics in coupled networks can synchronize or differ, revealing the mechanisms behind these phases through real data analysis and a two-layer network model, with implications for multi-layer epidemic control.

Contribution

It introduces a coupled two-layer network model to explain synchronized and mixed epidemic outbreaks, supported by theoretical analysis and real data.

Findings

Synchronized outbreaks occur in networks with similar average degrees.

Mixed outbreaks are more common when networks have different average degrees.

Coupling can suppress mixed outbreaks and promote synchronized ones.

Abstract

Epidemic spreading has been studied for a long time and most of them are focused on the growing aspect of a single epidemic outbreak. Recently, we extended the study to the case of recurrent epidemics (Sci. Rep. {\bf 5}, 16010 (2015)) but limited only to a single network. We here report from the real data of coupled regions or cities that the recurrent epidemics in two coupled networks are closely related to each other and can show either synchronized outbreak phase where outbreaks occur simultaneously in both networks or mixed outbreak phase where outbreaks occur in one network but do not in another one. To reveal the underlying mechanism, we present a two-layered network model of coupled recurrent epidemics to reproduce the synchronized and mixed outbreak phases. We show that the synchronized outbreak phase is preferred to be triggered in two coupled networks with the same average degree while the mixed outbreak phase is preferred for the case with different average degrees. Further, we show that the coupling between the two layers is preferred to suppress the mixed outbreak phase but enhance the synchronized outbreak phase. A theoretical analysis based on microscopic Markov-chain approach is presented to explain the numerical results. This finding opens a new window for studying the recurrent epidemics in multi-layered networks.