  In the real world, many complex systems interact with other systems. In
addition, the intra- or inter-systems for the spread of information about
infectious diseases and the transmission of infectious diseases are often not
random, but with direction. Hence, in this paper, we build epidemic model based
on an interconnected directed network, which can be considered as the
generalization of undirected networks and bipartite networks. By using the
mean-field approach, we establish the Susceptible-Infectious-Susceptible model
on this network. We theoretically analyze the model, and obtain the basic
reproduction number, which is also the generalization of the critical number
corresponding to undirected or bipartite networks. And we prove the global
stability of disease-free and endemic equilibria via the basic reproduction
number as a forward bifurcation parameter. We also give a condition for
epidemic prevalence only on a single subnetwork. Furthermore, we carry out
numerical simulations, and find that the independence between each node's in-
and out-degrees greatly reduce the impact of the network's topological
structure on disease spread.
