Peer-to-peer (P2P) networking has the potential of providing wide channels for file exchange. At the same time, P2P is prone to the proliferation of viruses. Peer trust reputation can be used to prevent virus dissemination. However, when viruses have infectious properties, peer reputation may not be enough to limit their proliferation. This letter shows the inefficiency of simple peer reputation to bound epidemics in an infectious environment and introduces a trust management algorithm that uses the combination of trust values of peers and infection values of both peers and content to bound the proliferation of viruses in P2P networks. The proposed trust management scheme can bound virus proliferation to a small number of peers without inhibiting file-download activity.