A New Model for Capturing the Spread of Computer Viruses on Complex-Networks

Based on complex network, this paper proposes a novel computer virus propagation model which is motivated by the traditional SEIRQ model. A systematic analysis of this new model shows that the virus-free equilibrium is globally asymptotically stable when its basic reproduction is less than one, and the viral equilibrium is globally attractive when the basic reproduction is greater than one. Some numerical simulations are finally given to illustrate the main results, implying that these results are applicable to depict the dynamics of virus propagation.

[1]  Meng Yang,et al.  A modified SIS model with an infective medium on complex networks and its global stability , 2011 .

[2]  Chenquan Gan,et al.  An epidemic model of computer viruses with vaccination and generalized nonlinear incidence rate , 2013, Appl. Math. Comput..

[3]  Yi Wang,et al.  Global analysis of an SIS model with an infective vector on complex networks , 2012 .

[4]  Luosheng Wen,et al.  Global asymptotic stability and a property of the SIS model on bipartite networks , 2012 .

[5]  Lu-Xing Yang,et al.  A delayed computer virus propagation model and its dynamics , 2012 .

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

[7]  Laurent Massoulié,et al.  Thresholds for virus spread on networks , 2006, valuetools '06.

[8]  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 .

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

[10]  M. Small,et al.  Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Qingyi Zhu,et al.  Optimal control of computer virus under a delayed model , 2012, Appl. Math. Comput..

[12]  José Roberto Castilho Piqueira,et al.  Dynamic models for computer viruses , 2008, Comput. Secur..

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

[14]  William M. Spears,et al.  A unified prediction of computer virus spread in connected networks , 2002 .

[15]  A. Barabasi,et al.  Halting viruses in scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Z. Duan,et al.  An SIS model with infective medium on complex networks , 2008 .

[17]  Claudio Castellano,et al.  Thresholds for epidemic spreading in networks , 2010, Physical review letters.

[18]  J. Yorke,et al.  A Deterministic Model for Gonorrhea in a Nonhomogeneous Population , 1976 .

[19]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[20]  Chenquan Gan,et al.  The spread of computer virus under the effect of external computers , 2013 .

[21]  Navnit Jha,et al.  SEIQRS model for the transmission of malicious objects in computer network , 2010 .

[22]  Guanrong Chen,et al.  Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Chenquan Gan,et al.  A propagation model of computer virus with nonlinear vaccination probability , 2014, Commun. Nonlinear Sci. Numer. Simul..

[24]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[25]  Chenquan Gan,et al.  Epidemics of computer viruses: A complex-network approach , 2013, Appl. Math. Comput..

[26]  Alberto d’Onofrio,et al.  A note on the global behaviour of the network-based SIS epidemic model , 2008 .

[27]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

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

[29]  Jeffrey O. Kephart,et al.  Directed-graph epidemiological models of computer viruses , 1991, Proceedings. 1991 IEEE Computer Society Symposium on Research in Security and Privacy.