  The disease spreading on complex networks is studied in SIR model.
Simulations on empirical complex networks reveal two specific regimes of
disease spreading: local containment and epidemic outbreak. The variables
measuring the extent of disease spreading are in general characterized by a
bimodal probability distribution. Phase diagrams of disease spreading for
empirical complex networks are introduced. A theoretical model of disease
spreading on m-ary tree is investigated both analytically and in simulations.
It is shown that the model reproduces qualitative features of phase diagrams of
disease spreading observed in empirical complex networks. The role of tree-like
structure of complex networks in disease spreading is discussed.
