Abstract
Unlike new medical procedures, new antivirus software can be disseminated rapidly through the Internet and takes effect immediately after it is run. As a result, a considerable number of infected computers can be cured almost simultaneously. Consequently, it is of practical importance to understand how pulse treatment affects the spread of computer viruses. For this purpose, an impulsive malware propagation model is proposed. To the best of our knowledge, this is the first computer virus model that takes into account the effect of pulse treatment. The dynamic properties of this model are investigated comprehensively. Specifically, it is found that (a) the virus-free periodic solution is globally asymptotically stable when the basic reproduction ratio (BRR) is less than unity, (b) infections are permanent when the BRR exceeds unity, and (c) a locally asymptotically stable viral periodic solution bifurcates from the virus-free periodic solution when the BRR goes through unity. A close inspection of the influence of different model parameters on the BRR allows us to suggest some feasible measures of eradicating electronic infections.
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Acknowledgments
The authors wish to express sincere gratitude to the two anonymous reviewers for their valuable suggestions that have greatly improved the quality of this paper. This work is supported by the Natural Science Foundation of China (Grant No. 10771227) and Doctorate Foundation of Educational Ministry of China (Grant No. 20110191110022).
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Yang, LX., Yang, X. The pulse treatment of computer viruses: a modeling study. Nonlinear Dyn 76, 1379–1393 (2014). https://doi.org/10.1007/s11071-013-1216-x
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DOI: https://doi.org/10.1007/s11071-013-1216-x