Reverse-feeding effect of epidemic by propagators in two-layered networks

Epidemic spreading has been studied for a long time and is currently focused on the spreading of multiple pathogens,especially in multiplex networks. However, little attention has been paid to the case where the mutual influence between different pathogens comes from a fraction of epidemic propagators, such as bisexual people in two separated groups of heterosexual and homosexual people. We here study this topic by presenting a network model of two layers connected by impulsive links, in contrast to the persistent links in each layer. We let each layer have a distinct pathogen and their interactive infection is implemented by a fraction of propagators jumping between the corresponding pairs of nodes in the two layers. By this model we show that(i) the propagators take the key role to transmit pathogens from one layer to the other,which significantly influences the stabilized epidemics;(ii) the epidemic thresholds will be changed by the propagators;and(iii) a reverse-feeding effect can be expected when the infective rate is smaller than its threshold of isolated spreading.A theoretical analysis is presented to explain the numerical results.