Impact of discontinuous antivirus strategy in a computer virus model with the point to group

Abstract In this paper, by considering the development of antivirus software always lags behind the emergence of new virus and the point-to-group information propagation mode, a new computer virus model with point to group and discontinuous anti-virus strategy is presented. To the best of our knowledge, this is the first computer virus model that takes into account the effect of discontinuous anti-virus strategy. The dynamic properties of this model are investigated comprehensively. Specifically, it is found that in the case that the equilibrium is asymptotically stable, the convergence to the equilibrium can actually be achieved in finite time, and the time can be estimated in terms of the model parameters, the initial number of the uninfected computer and latent computer and the initial anti-virus strength, which means the virus in the network can be controlled or eliminated in finite time by increasing the anti-virus strength. Finally, two illustrative examples are also given to support the theoretical results.

[1]  Lu-Xing Yang,et al.  A mixing propagation model of computer viruses and countermeasures , 2013 .

[2]  X. Liao,et al.  Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus , 2012 .

[3]  Lu-Xing Yang,et al.  A new epidemic model of computer viruses , 2014, Commun. Nonlinear Sci. Numer. Simul..

[4]  Hua Yuan,et al.  Network virus-epidemic model with the point-to-group information propagation , 2008, Appl. Math. Comput..

[5]  J. Aubin,et al.  Differential inclusions set-valued maps and viability theory , 1984 .

[6]  Ge Yu,et al.  Hopf bifurcation in an Internet worm propagation model with time delay in quarantine , 2013, Math. Comput. Model..

[7]  Lu-Xing Yang,et al.  A computer virus model with graded cure rates , 2013 .

[8]  Bimal Kumar Mishra,et al.  Fixed period of temporary immunity after run of anti-malicious software on computer nodes , 2007, Appl. Math. Comput..

[9]  Bimal Kumar Mishra,et al.  Fuzzy epidemic model for the transmission of worms in computer network , 2010 .

[10]  R.W. Thommes,et al.  Modeling Virus Propagation in Peer-to-Peer Networks , 2005, 2005 5th International Conference on Information Communications & Signal Processing.

[11]  Erol Gelenbe.  Dealing with software viruses: A biological paradigm , 2007, Inf. Secur. Tech. Rep..

[12]  Cynthia A. Phillips,et al.  Constructing Computer Virus Phylogenies , 1996, J. Algorithms.

[13]  Xiaofan Yang,et al.  The spread of computer viruses under the influence of removable storage devices , 2012, Appl. Math. Comput..

[14]  Lu-Xing Yang,et al.  Propagation Behavior of Virus Codes in the Situation That Infected Computers Are Connected to the Internet with Positive Probability , 2012 .

[15]  M. Forti,et al.  Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations , 2006 .

[16]  Xiaoming Fan,et al.  Global stability of deterministic and stochastic multigroup SEIQR models in computer network , 2013 .

[17]  Jiming Liu,et al.  A novel computer virus propagation model and its dynamics , 2012, Int. J. Comput. Math..

[18]  Chunming Zhang,et al.  Hopf Bifurcation of an Improved SLBS Model under the Influence of Latent Period , 2013 .

[19]  Francesca Maria Ceragioli,et al.  Discontinuous ordinary differential equations and stabilization , 2000 .

[20]  Huanhe Dong,et al.  Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation , 2012 .

[21]  R. Robinson,et al.  An Introduction to Dynamical Systems: Continuous and Discrete , 2004 .

[22]  Jooyoung Park,et al.  Investigation of the C-SEIRA model for controlling malicious code infection in computer networks , 2015 .

[23]  A. Bacciotti,et al.  Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions , 1999 .

[24]  Wei Wu,et al.  A Smoothing Interval Neural Network , 2012 .

[25]  Erol Gelenbe.  Keeping Viruses Under Control , 2005, ISCIS.