A unified framework of mutual influence between two pathogens in multiplex networks

There are many evidences to show that different pathogens may interplay each other and cause a variety of mutual influences of epidemics in multiplex networks, but it is still lack of a framework to unify all the different dynamic outcomes of the interactions between the pathogens. We here study this problem and first time present the concept of state-dependent infectious rate, in contrast to the constant infectious rate in previous studies. We consider a model consisting of a two-layered network with one pathogen on the first layer and the other on the second layer, and show that all the different influences between the two pathogens can be given by the different range of parameters in the infectious rates, which includes the cases of mutual enhancement, mutual suppression, and even initial cooperation (suppression) induced final suppression (acceleration). A theoretical analysis is present to explain the numerical results.