Synchronized and mixed outbreaks of coupled recurrent epidemics.

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. 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 pattern where outbreaks occur simultaneously in both networks or mixed outbreak pattern 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 patterns. We show that the synchronized outbreak pattern is preferred to be triggered in two coupled networks with the same average degree while the mixed outbreak pattern is likely to show for the case with different average degrees. Further, we show that the coupling between the two layers tends to suppress the mixed outbreak pattern but enhance the synchronized outbreak pattern. 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.