Stability Analysis of a Worm Propagation Model with Quarantine and Vaccination

Internet worms pose a serious threat to the Internet security. In order to effectively defend against Internet worms, this paper proposes a novel epidemic ＂e-SEIQV＂ model with quarantine and vaccination. Using this ＂e-SEIQV＂ model, we obtain the basic reproduction number for deter- mining whether the worm dies out completely. The global stability of the worm-free equilibrium and the local stability of endemic equilibrium are proved, and determined by the basic reproduction number. Besides the impact of different parameters of this model is studied. Simulation results show that the number of susceptible and infected hosts are consistent with the theoretical analysis. The model provides a theoretical foundation for controlling and forecasting Internet worms.

[1]  Shigui Ruan,et al.  Uniform persistence and flows near a closed positively invariant set , 1994 .

[2]  Fangwei Wang,et al.  Stability analysis of a SEIQV epidemic model for rapid spreading worms , 2010, Comput. Secur..

[3]  Eduardo Feitosa,et al.  An orchestration approach for unwanted Internet traffic identification , 2012, Comput. Networks.

[4]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[5]  James S. Muldowney,et al.  Compound matrices and ordinary differential equations , 1990 .

[6]  Huizhong Yang,et al.  Dynamics of a Delayed Model for the Transmission of Malicious Objects in Computer Network , 2014, TheScientificWorldJournal.

[7]  Seong-Moo Yoo,et al.  Stability analysis of VEISV propagation modeling for network worm attack , 2012 .

[8]  Xun Wang,et al.  On detecting active worms with varying scan rate , 2011, Comput. Commun..

[9]  R. Ruth,et al.  Stability of dynamical systems , 1988 .

[10]  Muhammad Ozair,et al.  Analysis of vector-host model with latent stage having partial immunity , 2014 .

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

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

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

[14]  Ge Yu,et al.  Pulse quarantine strategy of internet worm propagation: Modeling and analysis , 2012, Comput. Electr. Eng..

[15]  Lu-Xing Yang,et al.  A novel computer virus model and its dynamics , 2012 .

[16]  M. Li,et al.  Global dynamics of a SEIR model with varying total population size. , 1999, Mathematical Biosciences.

[17]  Juan Liu,et al.  Hopf Bifurcation in a Delayed SEIQRS Model for the Transmission of Malicious Objects in Computer Network , 2014, J. Appl. Math..

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

[19]  Lu-Xing Yang,et al.  Towards the Epidemiological Modeling of Computer Viruses , 2012 .

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

[21]  Bimal Kumar Mishra,et al.  Dynamic model of worms with vertical transmission in computer network , 2011, Appl. Math. Comput..

[22]  David Moore,et al.  Code-Red: a case study on the spread and victims of an internet worm , 2002, IMW '02.

[23]  Maobin Yang,et al.  An SLBRS Model with Vertical Transmission of Computer Virus over the Internet , 2012 .

[24]  James S. Muldowney,et al.  A Geometric Approach to Global-Stability Problems , 1996 .

[25]  Tarik Taleb,et al.  Combating against internet worms in large-scale networks: an autonomic signature-based solution , 2009, Secur. Commun. Networks.

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

[27]  Jianguo Ren,et al.  Dynamics of a Delay-Varying Computer Virus Propagation Model , 2012 .