  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.
