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In this paper, we formulate an analytical model to characterize the spread of malware in decentralized, Gnutella type peer-to-peer (P2P) networks and study the dynamics associated with the spread of malware. Using a compartmental model, we derive the system parameters or network conditions under which the P2P network may reach a malware free equilibrium. The model also evaluates the effect of control strategies like node quarantine on stifling the spread of malware. The model is then extended to consider the impact of P2P networks on the malware spread in networks of smart cell phones.