In this paper we present analytical techniques that can be used to better understand the behavior of malware, a generic term that refers to all kinds of malicious software programs propagating on the Internet, such as e-mail viruses and worms. We develop a modeling methodology based on Interactive Markov Chains that is able to capture many aspects of the problem, especially the impact of the underlying topology on the spreading characteristics of malware. We propose numerical methods to obtain useful bounds and approximations in the case of very large systems, validating our results through simulation. An analytic methodology represents a fundamentally important step in the development of effective countermeasures for future malware activity. Furthermore, we believe our approach can help to understand a wide range of "dynamic interactions on networks", such as routing protocols and peer-to-peer applications.
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