Global behavior of epidemic transmission on heterogeneous networks via two distinct routes

In the study of epidemic spreading two natural questions are: whether the spreading of epidemics on heterogenous networks have multiple routes, and whether the spreading of an epidemic is a local or global behavior? In this paper, we answer the above two questions by studying the SIS model on heterogenous networks, and give the global conditions for the endemic state when two distinct routes with uniform rate of infection are considered. The analytical results are also verified by numerical simulations.