Epidemic Dynamics of Interacting Two Particle Species on Scale-free   Networks
  We study the non-equilibrium phase transition in a model for epidemic spreading on scale-free networks. The model consists of two particle species $A$ and $B$, and the coupling between them is taken to be asymmetric; $A$ induces $B$ while $B$ suppresses $A$. This model describes the spreading of an epidemic on networks equipped with a reactive immune system. We present analytic results on the phase diagram and the critical behavior, which depends on the degree exponent $\gamma$ of the underlying scale-free networks. Numerical simulation results that support the analytic results are also presented. 
Yong-Yeol Ahn, Naoki Masuda, Hawoong Jeong, Jae Dong Noh