Abstract
Known as the plague of the Internet age, malware causes mass economic losses. A computer worm is a kind of stand-alone malware which spreads itself to neighboring nodes by exploiting vulnerabilities. Computer worms are an extremely important aspect of computer security, and understanding their spread and extent is an important component of any defensive strategy. Epidemiological models have been proposed to deal with this issue. In order to establish one such here, the nodes on the network are divided into three compartments: susceptible nodes (S), latent nodes (L) and breaking-out nodes (B). By the compartment method, a discrete model of computer worm prevalence is established. This model includes a reintroduction parameter which models the users’ security awareness. This is a more realistic model of computer worm spread than the ones in literature, and it can be used to understand the influence of security awareness on the propagation of computer worms. To be specific, the dynamics of this model is analyzed by use of the stability theory concerning difference equations. First, the basic reproduction number determining the behavior of worm propagation on the network is calculated. Then, the asymptotic stability of the worm-free equilibrium is proved if the threshold is below unity. Finally, the asymptotic stability of the worm equilibrium is shown by numerical simulations provided the threshold exceeds unity.
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Acknowledgments
We thank the editors and the anonymous reviewers for their valuable comments, which helped us to improve the manuscript. This research was funded by Project Supported by Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ1500904, KJ1500926, KJ1401307), Research Project of Humanities and Social Sciences of Ministry of Education of China (Grant No. 15YJC790061), and Fund of the Foundation and Cutting-edge Research Plan of Chongqing Science and Technology Committee(Grant No. cstc2014jcyjA40024, cstc2014jcyjA40007).
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Liu, W., Liu, C., Liu, X. (2015). A Discrete Dynamic Model for Computer Worm Propagation. In: Bohner, M., Ding, Y., Došlý, O. (eds) Difference Equations, Discrete Dynamical Systems and Applications. Springer Proceedings in Mathematics & Statistics, vol 150. Springer, Cham. https://doi.org/10.1007/978-3-319-24747-2_9
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