Nonlinear Dynamics

, Volume 76, Issue 2, pp 1379–1393 | Cite as

The pulse treatment of computer viruses: a modeling study

Original Paper


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.


Computer virus Epidemic model Pulse treatment  Basic reproduction ratio Virus-free periodic solution Global stability Viral permanence Viral periodic solution Supercritical bifurcation 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.College of Computer ScienceChongqing UniversityChongqingChina
  2. 2.College of Mathematics and StatisticsChongqing UniversityChongqingChina

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