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P2P worms pose heavy threatens to P2P networks. P2P worms exploit common vulnerabilities in member hosts of a P2P network and spread topologically in the P2P network, a potentially more effective strategy than random scanning for locating victims. Considering that the topology of P2P networks has important effect on P2P active worm spreading, it is very difficult to model propagation of P2P active worms. For this reason, so far few propagation models are proposed. In this paper, we propose a propagation model of active worms in P2P networks based the discrete-time method. The analysis on simulation results shows that there exists some threshold value during spreading of active worms and different infection strategies result in different infection results in P2P networks.