The combined impact of external computers and network topology on the spread of computer viruses

REFERENCES

• R. Albert and A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys. 74(1) (2002), pp. 47–97. doi: 10.1103/RevModPhys.74.47
   Web of Science ®Google Scholar
• M. Barthélemy, A. Barrat, R. Pastor-Satorras, and A. Vespignani, Velocity and hierarchical spread of epidemic outbreaks in scale-free networks, Phys. Rev. Lett. 92 (2004), Article ID 178701, 4pp. doi: 10.1103/PhysRevLett.92.178701
   Web of Science ®Google Scholar
• L. Billings, W.M. Spears, and I.B. Schwartz, A unified prediction of computer virus spread in connected networks, Phys. Lett. A 297(3–4) (2002), pp. 261–266. doi: 10.1016/S0375-9601(02)00152-4
   Web of Science ®Google Scholar
• M. Boguñá, R. Pastor-Satorras, and A. Vespignani, Absence of epidemic threshold in scale-free networks with degree correlations, Phys. Rev. Lett. 90(2) (2003), Article ID 028701, 4pp. doi: 10.1103/PhysRevLett.90.028701
   PubMed Web of Science ®Google Scholar
• C. Castellano and R. Pastor-Satorras, Thresholds for epidemic spreading in networks, Phys. Rev. Lett. 105(21) (2010), Article ID 218701, 4pp. doi: 10.1103/PhysRevLett.105.218701
   Web of Science ®Google Scholar
• L.-C. Chen and K.M. Carley, The impact of countermeasure propagation on the prevalence of computer viruses, IEEE Trans. Syst. Man Cybern. B, Cybern. 34(2) (2004), pp. 823–833. doi: 10.1109/TSMCB.2003.817098
   PubMed Web of Science ®Google Scholar
• F. Cohen, Computer viruses: Theory and experiments, Comput. Secur. 6(1) (1987), pp. 22–35. doi: 10.1016/0167-4048(87)90122-2
   Google Scholar
• Z. Dezsö and A.-L. Barabási, Halting viruses in scale-free networks, Phys. Rev. E 65(5) (2002), Article ID 055103, 4pp. doi: 10.1103/PhysRevE.65.055103
   Web of Science ®Google Scholar
• T. Dong, X. Liao, and H. Li, Stability and Hopf bifurcation in a computer virus model with multistate antivirus, Abstr. Appl. Anal. 2012 (2012), Article ID 841987, 16pp.
   Web of Science ®Google Scholar
• A. d'Onofrio, A note on the global behavior of the network-based SIS epidemic model, Nonlinear Anal. RWA 9(4) (2008), pp. 1567–1572. doi: 10.1016/j.nonrwa.2007.04.001
   Web of Science ®Google Scholar
• M. Draief, A. Ganesh, and L. Massouilié, Thresholds for virus spread on networks, Ann. Appl. Probab. 18(2) (2008), pp. 359–378. doi: 10.1214/07-AAP470
   Web of Science ®Google Scholar
• M. Faloutsos, P. Faloutsos, and C. Faloutsos, On power-law relationships of the Internet topology, ACM SIGCOMM Comput. Commun. Rev. 29(4) (1999), pp. 251–262. doi: 10.1145/316194.316229
   Google Scholar
• L. Feng, X. Liao, H. Li, and Q. Han, Hopf bifurcation analysis of a delayed viral infection model in computer networks, Math. Comput. Modelling 56(7–8) (2012), pp. 167–179. doi: 10.1016/j.mcm.2011.12.010
   Web of Science ®Google Scholar
• X. Fu, M. Small, D.M. Walker, and H. Zhang, Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization, Phys. Rev. E 77 (2008), Article ID 036113, 8pp. doi: 10.1103/PhysRevE.77.036113
   PubMed Web of Science ®Google Scholar
• C. Gan, X. Yang, W. Liu, and Q. Zhu, A propagation model of computer virus with nonlinear vaccination probability, Commun. Nonlinear Sci. Numer. Simul. 19(1) (2014), pp. 92–100. doi: 10.1016/j.cnsns.2013.06.018
   Web of Science ®Google Scholar
• C. Gan, X. Yang, Q. Zhu, J. Jin, and L. He, The spread of computer virus under the effect of external computers, Nonlinear Dyn. 73(3) (2013), pp. 1615–1620. doi: 10.1007/s11071-013-0889-5
   Web of Science ®Google Scholar
• C. Gan, X. Yang, W. Liu, Q. Zhu, and X. Zhang, Propagation of computer virus under human intervention: A dynamical model, Discrete Dyn. Nat. Soc. 2012 (2012), Article ID 106950, 8pp.
   Web of Science ®Google Scholar
• C. Gan, X. Yang, W. Liu, Q. Zhu, and X. Zhang, An epidemic model of computer viruses with vaccination and generalized nonlinear incidence rate, Appl. Math. Comput. 222(1) (2013), pp. 265–274. doi: 10.1016/j.amc.2013.07.055
   Web of Science ®Google Scholar
• C. Griffin and R. Brooks, A note on the spread of worms in scale-free networks, IEEE Trans. Syst. Man Cybern. B Cybern. 36(1) (2006), pp. 198–202. doi: 10.1109/TSMCB.2005.854498
   PubMed Web of Science ®Google Scholar
• X. Han and Q. Tan, Dynamical behavior of computer virus on Internet, Appl. Math. Comput. 217(6) (2010), pp. 2520–2526. doi: 10.1016/j.amc.2010.07.064
   Web of Science ®Google Scholar
• J.M. Heffernan, R.J. Smith, and L.M. Wahl, Perspectives on the basic reproductive ratio, J. R. Soc. Interface 2(4) (2005), pp. 281–293. doi: 10.1098/rsif.2005.0042
   PubMed Web of Science ®Google Scholar
• M. Karsai, M. Kivelä, R.K. Pan, K. Kaski, J. Kertész, A.-L. Barabási, J. Saramäki, Small but slow world: How network topology and burstiness slow down spreading, Phys. Rev. E 83(2) (2011), Article ID 025102, 4pp. doi: 10.1103/PhysRevE.83.025102
   Web of Science ®Google Scholar
• J.O. Kephart and S.R. White, Directed-graph epidemiological models of computer viruses, Proceedings of the 1991 IEEE Computer Society Symposium on Research in Security and Privacy, Oakland, CA, 1991, pp. 343–359.
   Google Scholar
• J.O. Kephart and S.R. White, Measuring and modeling computer virus prevalence, Proceedings of the 1993 IEEE Symposium on Security and Privacy, Oakland, CA, 1993, pp. 2–15.
   Google Scholar
• A. Lajmanovich and J.A. Yorke, A deterministic model for gonorrhea in anonhomogenous population, Math. Biosci. 28(3–4) (1976), pp. 221–236. doi: 10.1016/0025-5564(76)90125-5
   Google Scholar
• A.L. Lloyd and R.M. May, How viruses spread among computers and people, Science 292(5520) (2001), pp. 1316–1317. doi: 10.1126/science.1061076
   PubMed Web of Science ®Google Scholar
• B.K. Mishra and N. Jha, Fixed period of temporary immunity after run of anti-malicious software on computer nodes, Appl. Math. Comput. 190(2) (2007), pp. 1207–1212. doi: 10.1016/j.amc.2007.02.004
   Web of Science ®Google Scholar
• B.K. Mishra and S.K. Pandey, Dynamic model of worms with vertical transmission in computer network, Appl. Math. Comput. 217(21) (2011), pp. 8438–8446. doi: 10.1016/j.amc.2011.03.041
   Web of Science ®Google Scholar
• B.K. Mishra and D.K. Saini, SEIRS epidemic model with delay for transmission of malicious objects in computer network, Appl. Math. Comput. 188(2) (2007), pp. 1476–1482. doi: 10.1016/j.amc.2006.11.012
   Web of Science ®Google Scholar
• B.K. Mishra and D.K. Saini, SEIQRS model for the transmission of malicious objects in computer network, Appl. Math. Model. 34(3) (2010), pp. 710–715. doi: 10.1016/j.apm.2009.06.011
   Web of Science ®Google Scholar
• Y. Moreno, R. Pastor-Satorras, and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks, Eur. Phys. J. B 26(4) (2002), pp. 521–529.
   Web of Science ®Google Scholar
• W.H. Murray, The application of epidemiology to computer viruses, Comput. Secur. 7(2) (1988), pp. 130–150. doi: 10.1016/0167-4048(88)90327-6
   Google Scholar
• R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett. 86(14) (2001), pp. 3200–3203. doi: 10.1103/PhysRevLett.86.3200
   PubMed Web of Science ®Google Scholar
• R. Pastor-Satorras and A. Vespignani, Epidemic dynamics and endemic states in complex networks, Phys. Rev. E 63(6) (2001), Article ID 066117, 8pp. doi: 10.1103/PhysRevE.63.066117
   PubMed Web of Science ®Google Scholar
• R. Pastor-Satorras and A. Vespignani, Immunization of complex networks, Phys. Rev. E 65(3) (2002), Article ID 036104, 8pp.
   Google Scholar
• J.R.C. Piqueira and V.O. Araujo, A modified epidemiological model for computer viruses, Appl. Math. Comput. 213(2) (2009), pp. 355–360. doi: 10.1016/j.amc.2009.03.023
   Web of Science ®Google Scholar
• J.R.C. Piqueira, A.A. de Vasconcelos, C.E.C.J. Gabriel, and V.O. Araujo, Dynamic models for computer viruses, Comput. Secur. 27(7–8) (2008), pp. 355–359. doi: 10.1016/j.cose.2008.07.006
   Web of Science ®Google Scholar
• J. Ren, X. Yang, Q. Zhu, L.X. Yang, and C. Zhang, A novel computer virus model and its dynamics, Nonliear Anal. RWA 13(1) (2012), pp. 376–384. doi: 10.1016/j.nonrwa.2011.07.048
   Web of Science ®Google Scholar
• J. Ren, X. Yang, L.-X. Yang, Y. Xu, and F. Yang, A delayed computer virus propagation model and its dynamics, Chaos Solitons Fractals 45(1) (2012), pp. 74–79. doi: 10.1016/j.chaos.2011.10.003
   Web of Science ®Google Scholar
• H.J. Shi, Z.S. Duan, and G.R. Chen, An SIS model with infective medium on complex networks, Phys. A 387(8–9) (2008), pp. 2133–2144. doi: 10.1016/j.physa.2007.11.048
   Web of Science ®Google Scholar
• P. Szor, The Art of Computer Virus Research and Defense, Addison-Wesley Professional, Boston, MA, 2005.
   Google Scholar
• H.R. Thieme, Asymptotically autonomous differential equations in the plane, Rocky Mountain J. Math. 24 (1994), pp. 351–380. doi: 10.1216/rmjm/1181072470
   Web of Science ®Google Scholar
• O.A. Toutonji, S.-M. Yoo, and M. Park, Stability analysis of VEISV propagation modeling for network worm attack, Appl. Math. Model. 36(6) (2012), pp. 2751–2761. doi: 10.1016/j.apm.2011.09.058
   Web of Science ®Google Scholar
• P. Van Mieghem, J. Omic, and R. Kooij, Virus spread in networks, IEEE/ACM Trans. Netw. 17(1) (2009), pp. 1–14. doi: 10.1109/TNET.2008.925623
   Web of Science ®Google Scholar
• L.S. Wen and J. Zhong, Global asymptotic stability and a property of the SIS model on bipartite networks, Nonlinear Anal. RWA 13(2) (2012), pp. 967–976. doi: 10.1016/j.nonrwa.2011.09.003
   Web of Science ®Google Scholar
• J.C. Wierman and D.J. Marchette, Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction, Comput. Statist. Data Anal. 45(1) (2004), pp. 3–23. doi: 10.1016/S0167-9473(03)00113-0
   Web of Science ®Google Scholar
• L.-X. Yang and X. Yang, The spread of computer viruses under the influence of removable storage devices, Appl. Math. Comput. 219(8) (2012), pp. 3914–3922. doi: 10.1016/j.amc.2012.10.027
   Web of Science ®Google Scholar
• L.-X. Yang and X. Yang, A new epidemic model of computer viruses, Commun. Nonlinear Sci. Numer. Simulat. 19(6) (2014), pp. 1935–1944. doi: 10.1016/j.cnsns.2013.09.038
   Web of Science ®Google Scholar
• L.-X. Yang and X. Yang, The spread of computer viruses over a reduced scale-free network, Phys. A. 396(1) (2014), pp. 173–184. doi: 10.1016/j.physa.2013.11.026
   Web of Science ®Google Scholar
• L.-X. Yang, X. Yang, L. Wen, and J. Liu, Propagation behavior of virus codes in the situation that infected computers are connected to the Internet with positive probability, Discrete Dyn. Nat. Soc. 2012 (2012), Article ID 693695, 13pp.
   Web of Science ®Google Scholar
• L.-X. Yang, X. Yang, L. Wen, and J. Liu, A novel computer virus propagation model and its dynamics, Int. J. Comput. Math. 89(17) (2012), pp. 2307–2314. doi: 10.1080/00207160.2012.715388
   Web of Science ®Google Scholar
• L.-X. Yang, X. Yang, Q. Zhu, and L. Wen, A computer virus model with graded cure rates, Nonlinear Anal. RWA 14(1) (2013), pp. 414–422. doi: 10.1016/j.nonrwa.2012.07.005
   Web of Science ®Google Scholar
• L.-X. Yang, X. Yang, J. Liu, Q. Zhu, and C. Gan, Epidemics of computer viruses: A complex-network approach, Appl. Math. Comput. 219(16) (2013), pp. 8705–8717. doi: 10.1016/j.amc.2013.02.031
   Web of Science ®Google Scholar
• L.-X. Yang and X. Yang, The effect of infected external computers on the spread of viruses: A compartment modeling study, Phys. A 392(24) (2013), pp. 6523–6535. doi: 10.1016/j.physa.2013.08.024
   Web of Science ®Google Scholar
• M. Yang, G.R. Chen, and X.C. Fu, A modified SIS model with an infective medium on complex networks and its global stability, Phys. A 390(12) (2011), pp. 2408–2413. doi: 10.1016/j.physa.2011.02.007
   Web of Science ®Google Scholar
• X. Yang and L.-X. Yang, Towards the epidemiological modeling of computer viruses, Discrete Dyn. Nat. Soc. 2012 (2012), Article ID 259671, 11pp.
   Web of Science ®Google Scholar
• X. Yang, B.K. Mishra, and Y. Liu, Computer viruses: Theory, model, and methods, Discrete Dyn. Nat. Soc. 2012 (2012), Article ID 473508, 2pp.
   Web of Science ®Google Scholar
• M. Youssef and C. Scoglio, An individual-based approach to SIR epidemics in contact networks, J. Theor. Biol. 283(1) (2011), pp. 136–144. doi: 10.1016/j.jtbi.2011.05.029
   PubMed Web of Science ®Google Scholar
• H. Yuan and G. Chen, Network virus-epidemic model with the point-to-group information propagation, Appl. Math. Comput. 206(1) (2008), pp. 357–367. doi: 10.1016/j.amc.2008.09.025
   Web of Science ®Google Scholar
• H. Yuan, G. Chen, J. Wu, and H. Xiong, Towards controlling virus propagation in information systems with point-to-group information sharing, Decis. Supp. Syst. 48(1) (2009), pp. 57–68. doi: 10.1016/j.dss.2009.05.014
   Web of Science ®Google Scholar
• C. Zhang, Y. Zhao, Y. Wu, and S. Deng, A stochastic dynamic model of computer viruses, Discrete Dyn. Nat. Soc. 2012 (2012), Article ID 264874, 6pp.
   Web of Science ®Google Scholar
• T. Zhou, J.G. Liu, W.J. Bai, G.R. Chen, and B.H. Wang, Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity, Phys. Rev. E 74 (2006), Article ID 056109, 16pp.
   Web of Science ®Google Scholar
• G.H. Zhu, X.C. Fu, and G.R. Chen, Global attractivity of a network-based epidemic SIS model with nonlinear infectivity, Commun. Nonlinear Sci. Numer. Simul. 17(6) (2012), pp. 2588–2594. doi: 10.1016/j.cnsns.2011.08.039
   Web of Science ®Google Scholar
• Q. Zhu, X. Yang, and J. Ren, Modeling and analysis of the spread of computer virus, Commun. Nonlinear Sci. Numer. Simul. 17(12) (2012), pp. 5117–5124. doi: 10.1016/j.cnsns.2012.05.030
   Web of Science ®Google Scholar
• Q. Zhu, X. Yang, L.-X. Yang, and C. Zhang, Optimal control of computer virus under a delayed model, Appl. Math. Comput. 218(23) (2012), pp. 11613–11619. doi: 10.1016/j.amc.2012.04.092
   Web of Science ®Google Scholar
• Q. Zhu, X. Yang, L.-X. Yang, and X. Zhang, A mixing propagation model of computer viruses and countermeasures, Nonlinear Dyn. 73(3) (2013), pp. 1433–1441. doi: 10.1007/s11071-013-0874-z
   Web of Science ®Google Scholar