As the name suggests, epidemic protocols mimic spread of virus to implement broadcasting with high reliability and low communication cost in peer-to-peer (P2P) overlay networks. In this paper, we study the reliability of epidemic protocols in scale-free networks, an important class of P2P overlay network topologies. In order to improve the robustness of epidemic protocols, we optimize the basic epidemic protocol in the following two ways. One optimization is to introduce an adaptive mechanism that allows each node to retransmit a broadcast message adaptively to the environment. The other optimization is to modify the protocol such that nodes will forward broadcast messages preferentially to neighbor nodes of small degree. The usefulness of these optimizations is demonstrated through simulation results.