Today, the propagation of active worms in peer-to-peer (P2P) networks is a very serious issue. Therefore, studying the propagation behavior of active worms and modeling their proliferation is quite useful to employ an effective and low-cost defense strategy to reduce the rate of their propagation. The topology-aware worms use the information related to the topology and the network structure of their victims to propagate in the network. Recently, the logic matrix has been utilized to model the effect of worm propagation. In this paper, we use this kind of matrices to model the propagation of topology-aware active worms with emphasis on the impacts of the join and leave of hosts on the propagation ratio. Using a simulation model, we have studied and compared the impacts of the join and leave of hosts with the situations without them. The simulation results show the considerable impacts of join and leave on the propagation of worms.