Dynamic model of worms with vertical transmission in computer network

An e-epidemic SEIRS model for the transmission of worms in computer network through vertical transmission is formulated. It has been observed that if the basic reproduction number is less than or equal to one, the infected part of the nodes disappear and the worm dies out, but if the basic reproduct...

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Published in:	Applied mathematics and computation Vol. 217; no. 21; pp. 8438 - 8446
Main Authors:	Mishra, Bimal Kumar, Pandey, Samir Kumar
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Inc 01.07.2011 Elsevier
Subjects:	Computer network Computer networks Computer simulation Computer worms Dynamic models Endemic equilibrium Epidemic model Exact sciences and technology Global stability Mathematical analysis Mathematical models Mathematics Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Reproduction Sciences and techniques of general use Vertical transmission Worms Vertical transmission Computer network Epidemic model Global stability Worms Endemic equilibrium Transcendental equation Numerical method Stochastic method Equation system Non linear equation Numerical analysis Applied mathematics Algebraic equation Dynamic model Numerical stability
ISSN:	0096-3003, 1873-5649
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Abstract	An e-epidemic SEIRS model for the transmission of worms in computer network through vertical transmission is formulated. It has been observed that if the basic reproduction number is less than or equal to one, the infected part of the nodes disappear and the worm dies out, but if the basic reproduction number is greater than one, the infected nodes exists and the worms persist at an endemic equilibrium state. Numerical methods are employed to solve and simulate the system of equations developed. We have analyzed the behavior of the susceptible, exposed, infected and recovered nodes in the computer network with real parametric values.
AbstractList	An e-epidemic SEIRS model for the transmission of worms in computer network through vertical transmission is formulated. It has been observed that if the basic reproduction number is less than or equal to one, the infected part of the nodes disappear and the worm dies out, but if the basic reproduction number is greater than one, the infected nodes exists and the worms persist at an endemic equilibrium state. Numerical methods are employed to solve and simulate the system of equations developed. We have analyzed the behavior of the susceptible, exposed, infected and recovered nodes in the computer network with real parametric values.
Author	Pandey, Samir Kumar Mishra, Bimal Kumar
Author_xml	– sequence: 1 givenname: Bimal Kumar surname: Mishra fullname: Mishra, Bimal Kumar email: drbimalmishra@gmail.com organization: Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi 835215, India – sequence: 2 givenname: Samir Kumar surname: Pandey fullname: Pandey, Samir Kumar email: samir.phd2009@gmail.com organization: Department of Mathematics, Siksha ‘O’ Anusandhan University, Bhubaneswar, Orissa, India
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Cites_doi	10.1017/S0143385700001978 10.1103/PhysRevE.66.035101 10.1137/S0036141094266449 10.1214/07-AAP470 10.1098/rsif.2005.0051 10.1216/rmjm/1181073047 10.1137/S0036139999359860 10.1090/S0002-9939-1986-0822433-4 10.1016/j.amc.2006.09.062 10.1098/rspa.1933.0106 10.1098/rspa.1927.0118 10.1006/jdeq.1993.1097 10.1140/epjb/e2004-00119-8 10.1016/j.amc.2010.07.064 10.1109/RISP.1994.296580 10.1017/S014338570000626X 10.1155/2008/940526 10.1017/S144618110000345X 10.2307/2373413 10.1016/j.apm.2009.06.011 10.1109/TNET.2005.857113 10.21136/CMJ.1974.101253 10.1017/S030821050001920X 10.1016/j.amc.2007.02.004 10.1016/j.istr.2007.11.002 10.3844/jcssp.2005.31.34 10.1016/S0025-5564(99)00030-9 10.1007/BF02218848 10.1016/0022-247X(74)90084-5 10.1098/rspa.1932.0171 10.1016/j.amc.2006.11.012 10.1016/j.amc.2009.03.023 10.1109/6.275061 10.1016/j.amc.2008.09.025
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Keywords	Vertical transmission Computer network Epidemic model Global stability Worms Endemic equilibrium Transcendental equation Numerical method Stochastic method Equation system Non linear equation Numerical analysis Applied mathematics Algebraic equation Dynamic model Numerical stability
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References	Pugh, Robinson (b0225) 1983; 3 Keeling, Eames (b0080) 2005; 2 Newman, Forrest, Balthrop (b0090) 2002; 66 Richard, Mark (b0100) 2005 Han, Tan (b0245) 2010; 217 May, Lloyd (b0125) 2001; 64 Smith (b0215) 1986; 104 Kephart (b0110) 1995 Butler, Waltman (b0160) 1986; 96 Pastor-Satorras, Vespignani (b0120) 2002 S. Forest, S. Hofmeyr, A. Somayaji, T. Longstaff, Self-nonself discrimination in a computer, in: Proceeding of IEEE Symposium on Computer Security and Privacy, 1994, pp. 202–212. Kephart, White, Chess (b0075) 1993 Wang, Wang (b0050) 2003 Kermack, McKendrick (b0055) 1927; 115 Gelenbe, Kaptan, Wang (b0030) 2004; Vol. 3280 Zou, Gong, Towsley, Gao (b0070) 2005; 13 Martin (b0190) 1974; 45 Li, Muldowney (b0205) 1996; 27 Kermack, McKendrick (b0065) 1933; 141 Piqueira, Navarro, Monteiro (b0040) 2005; 1 Datta, Wang (b0130) 2005 Mishra, Saini (b0010) 2007; 187 Waltman (b0170) 1991 Li, Muldowney (b0200) 1994; 106 Muldowney (b0185) 1990; 20 . Hirsch (b0230) 1991; 11 Li, Smith, Wang (b0210) 2001; 62 Freedman, Tang, Ruan (b0165) 1994; 6 J.P. LaSalle, The stability of dynamical systems, CBMS-NSF Regional Conf. Ser. in Appl. Math. 25, SIAM, Philadelphia, 1976. Yuan, Chen (b0235) 2008; 206 Picqueria (b0240) 2009; 213 Kermack, McKendrick (b0060) 1932; 138 Chen, Jamil (b0145) 2006 Mishra, Jha (b0150) 2010; 34 Pugh (b0220) 1967; 89 Gelenbe (b0025) 2005; Vol. 3733 Moore, Shannon, Voelker, Savage (b0140) 2003 Gelenbe (b0020) 2007; 12 J.R.C. Piqueira, F.B. Cesar, Dynamic models for computer virus propagation, Math. Prob. Eng., 2008, Article ID 940526. Mishra, Jha (b0015) 2007; 190 Ma. M. Williamson, J. Leill, An Epidemiological Model of Virus Spread and cleanup, 2003 W.A. Coppel, Stability and asymptotic behavior of differential equations, Heath, Boston, 1965. Mishra, Saini (b0005) 2007; 188 Draief, Ganesh, Massouili (b0095) 2008; 18 Zou, Gong, Towsley (b0135) 2003 Madar, Kalisky, Cohen, Ben Avraham, Havlin (b0115) 2004; 38 Yan, Liu (b0105) 2006; 48 Li, Graef, Wang, Karsai (b0175) 1999; 160 Fiedler (b0180) 1974; 99 Zou (10.1016/j.amc.2011.03.041_b0135) 2003 Picqueria (10.1016/j.amc.2011.03.041_b0240) 2009; 213 Freedman (10.1016/j.amc.2011.03.041_b0165) 1994; 6 Gelenbe (10.1016/j.amc.2011.03.041_b0030) 2004; Vol. 3280 Mishra (10.1016/j.amc.2011.03.041_b0010) 2007; 187 Wang (10.1016/j.amc.2011.03.041_b0050) 2003 Gelenbe (10.1016/j.amc.2011.03.041_b0025) 2005; Vol. 3733 Muldowney (10.1016/j.amc.2011.03.041_b0185) 1990; 20 Li (10.1016/j.amc.2011.03.041_b0210) 2001; 62 Pastor-Satorras (10.1016/j.amc.2011.03.041_b0120) 2002 Chen (10.1016/j.amc.2011.03.041_b0145) 2006 10.1016/j.amc.2011.03.041_b0195 Kermack (10.1016/j.amc.2011.03.041_b0065) 1933; 141 10.1016/j.amc.2011.03.041_b0155 Mishra (10.1016/j.amc.2011.03.041_b0015) 2007; 190 Madar (10.1016/j.amc.2011.03.041_b0115) 2004; 38 Li (10.1016/j.amc.2011.03.041_b0175) 1999; 160 Kermack (10.1016/j.amc.2011.03.041_b0060) 1932; 138 Draief (10.1016/j.amc.2011.03.041_b0095) 2008; 18 Li (10.1016/j.amc.2011.03.041_b0200) 1994; 106 Newman (10.1016/j.amc.2011.03.041_b0090) 2002; 66 May (10.1016/j.amc.2011.03.041_b0125) 2001; 64 Waltman (10.1016/j.amc.2011.03.041_b0170) 1991 Fiedler (10.1016/j.amc.2011.03.041_b0180) 1974; 99 Kephart (10.1016/j.amc.2011.03.041_b0075) 1993 Moore (10.1016/j.amc.2011.03.041_b0140) 2003 Zou (10.1016/j.amc.2011.03.041_b0070) 2005; 13 Li (10.1016/j.amc.2011.03.041_b0205) 1996; 27 Han (10.1016/j.amc.2011.03.041_b0245) 2010; 217 Pugh (10.1016/j.amc.2011.03.041_b0225) 1983; 3 Kephart (10.1016/j.amc.2011.03.041_b0110) 1995 Butler (10.1016/j.amc.2011.03.041_b0160) 1986; 96 Datta (10.1016/j.amc.2011.03.041_b0130) 2005 Martin (10.1016/j.amc.2011.03.041_b0190) 1974; 45 Gelenbe (10.1016/j.amc.2011.03.041_b0020) 2007; 12 Mishra (10.1016/j.amc.2011.03.041_b0150) 2010; 34 Mishra (10.1016/j.amc.2011.03.041_b0005) 2007; 188 Kermack (10.1016/j.amc.2011.03.041_b0055) 1927; 115 Yuan (10.1016/j.amc.2011.03.041_b0235) 2008; 206 10.1016/j.amc.2011.03.041_b0035 Richard (10.1016/j.amc.2011.03.041_b0100) 2005 10.1016/j.amc.2011.03.041_b0085 10.1016/j.amc.2011.03.041_b0045 Keeling (10.1016/j.amc.2011.03.041_b0080) 2005; 2 Hirsch (10.1016/j.amc.2011.03.041_b0230) 1991; 11 Yan (10.1016/j.amc.2011.03.041_b0105) 2006; 48 Piqueira (10.1016/j.amc.2011.03.041_b0040) 2005; 1 Pugh (10.1016/j.amc.2011.03.041_b0220) 1967; 89 Smith (10.1016/j.amc.2011.03.041_b0215) 1986; 104
References_xml	– volume: 11 start-page: 443 year: 1991 end-page: 454 ident: b0230 article-title: Systems of differential equations that are competitive or cooperative. VI: A local Cr closing lemma for 3-dimensional systems publication-title: Ergodic Theory Dyn. Systems – volume: 96 start-page: 425 year: 1986 end-page: 430 ident: b0160 article-title: Persistence in dynamical systems publication-title: Proc. Amer. Math. Soc – start-page: 31 year: 1991 end-page: 40 ident: b0170 article-title: A brief survey of persistence in dynamical systems publication-title: Delay Differential Equations and Dynamical Systems – volume: 20 start-page: 857 year: 1990 end-page: 872 ident: b0185 article-title: Compound matrices and ordinary differential equations publication-title: Rocky Mountain J. Math – year: 1995 ident: b0110 article-title: A biologically inspired immune system for computers publication-title: Proc. Int. Joint Conf. Artif. Int. – volume: 3 start-page: 261 year: 1983 end-page: 313 ident: b0225 article-title: The publication-title: Ergodic Theory Dyn. Systems – start-page: 981 year: 2005 end-page: 985 ident: b0100 article-title: Modeling virus propagation in peer-to-peer networks publication-title: IEEE Int. Conf. Inform. Commun. Signal Process. – year: 2005 ident: b0130 article-title: The effectiveness of vaccinations on the spread of email-borne computer virus publication-title: IEEE CCECE/CCGEL – volume: 138 start-page: 55 year: 1932 end-page: 83 ident: b0060 article-title: Contributions of mathematical theory to epidemics publication-title: Proc. R. Soc. Lon. Ser. A – volume: 206 start-page: 357 year: 2008 end-page: 367 ident: b0235 article-title: Network virus epidemic model with the point – to – group information propagation publication-title: Appl. Math. Comput. – volume: 213 start-page: 355 year: 2009 end-page: 360 ident: b0240 article-title: A modified epidemiological model for computer viruses publication-title: Appl. Math. Comput. – volume: 6 start-page: 583 year: 1994 end-page: 600 ident: b0165 article-title: Uniform persistence and flows near a closed positively invariant set publication-title: J. Dyn. Differential Equations – reference: S. Forest, S. Hofmeyr, A. Somayaji, T. Longstaff, Self-nonself discrimination in a computer, in: Proceeding of IEEE Symposium on Computer Security and Privacy, 1994, pp. 202–212. – year: 2002 ident: b0120 publication-title: Epidemics and immunization in scale-free networks – volume: 45 start-page: 432 year: 1974 end-page: 454 ident: b0190 article-title: Logarithmic norms and projections applied to linear differential systems publication-title: J. Math. Anal. Appl – year: 2006 ident: b0145 article-title: Effectiveness of quarantine in worm epidemic publication-title: IEEE International Conference on Communications – volume: Vol. 3280 start-page: 667 year: 2004 end-page: 675 ident: b0030 article-title: Biological metaphors for agent behavior publication-title: Computer and Information Sciences – ISCIS 2004, 19th International Symposium – volume: 190 start-page: 1207 year: 2007 end-page: 1212 ident: b0015 article-title: Fixed period of temporary immunity after run of anti-malicious software on computer nodes publication-title: Appl. Math. Comput. – reference: W.A. Coppel, Stability and asymptotic behavior of differential equations, Heath, Boston, 1965. – volume: 34 start-page: 710 year: 2010 end-page: 715 ident: b0150 article-title: SEIQRS model for the transmission of malicious objects in computer network publication-title: Appl. Math. Model. – reference: J.R.C. Piqueira, F.B. Cesar, Dynamic models for computer virus propagation, Math. Prob. Eng., 2008, Article ID 940526. – volume: 13 start-page: 961 year: 2005 end-page: 974 ident: b0070 article-title: The monitoring and early detection of internet worms publication-title: IEEE/ACM Trans. Network – reference: . – volume: 160 start-page: 191 year: 1999 end-page: 213 ident: b0175 article-title: Global dynamics of an SEIR model with varying total population size publication-title: Math. Biosci. – volume: 2 start-page: 295 year: 2005 end-page: 307 ident: b0080 article-title: Network and epidemic models publication-title: J. Roy. Soc. Interf – volume: 217 start-page: 2520 year: 2010 end-page: 2526 ident: b0245 article-title: Dynamical behavior of computer virus on internet publication-title: Appl. Math. Comput. – volume: 62 start-page: 58 year: 2001 end-page: 69 ident: b0210 article-title: Global dynamics of an SEIR epidemic model with vertical transmission publication-title: SIAM J. Appl. Math – volume: 1 start-page: 31 year: 2005 end-page: 34 ident: b0040 article-title: Epidemiological models applied to virus in computer network publication-title: J. Comput. Sci – volume: 38 start-page: 269 year: 2004 end-page: 276 ident: b0115 article-title: Immunization and epidemic dynamics in complex networks publication-title: Eur. Phys. J. B – volume: 187 start-page: 929 year: 2007 end-page: 936 ident: b0010 article-title: Mathematical models on computer viruses publication-title: Appl. Math. Comput. – volume: 89 start-page: 956 year: 1967 end-page: 1009 ident: b0220 article-title: The closing lemma publication-title: Amer. J. Math – volume: 106 start-page: 27 year: 1994 end-page: 39 ident: b0200 article-title: On Bendixson’s criterion publication-title: J. Differential Equations – volume: 64 start-page: 1 year: 2001 end-page: 3 ident: b0125 article-title: Infection dynamics on scale-free networks publication-title: Phys. Rev. E – start-page: 61 year: 2003 end-page: 66 ident: b0050 article-title: Modeling the effect of timing parameters on virus propagation publication-title: 2003 ACM Workshop on Rapid Malcode – volume: 188 start-page: 1476 year: 2007 end-page: 1482 ident: b0005 article-title: SEIRS epidemic model with delay for transmission of malicious objects in computer network publication-title: Appl. Math. Comput. – volume: 66 start-page: 035101-1 year: 2002 end-page: 035101-4 ident: b0090 article-title: Email networks and the spread of computer virus publication-title: Phys. Rev. E – year: 2003 ident: b0140 article-title: Internet quarantine: requirements for containing self-propagating code publication-title: Proceeding of IEEE INFOCOM – volume: 12 start-page: 242 year: 2007 end-page: 250 ident: b0020 article-title: Dealing with software viruses: a biological paradigm publication-title: Inform. Secur. Tech. Rep – volume: 48 start-page: 119 year: 2006 end-page: 134 ident: b0105 article-title: SEIR epidemic model with delay publication-title: J. Aust. Math. Soc. Ser. B Appl. Math. – volume: Vol. 3733 year: 2005 ident: b0025 article-title: Keeping viruses under control publication-title: Computer and Information Sciences – ISCIS 2005, 20th International Symposium – reference: J.P. LaSalle, The stability of dynamical systems, CBMS-NSF Regional Conf. Ser. in Appl. Math. 25, SIAM, Philadelphia, 1976. – start-page: 20 year: 1993 end-page: 26 ident: b0075 article-title: Computers and epidemiology publication-title: IEEE Spectrum – reference: Ma. M. Williamson, J. Leill, An Epidemiological Model of Virus Spread and cleanup, 2003, – start-page: 51 year: 2003 end-page: 60 ident: b0135 article-title: Worm propagation modeling and analysis under dynamic quarantine defense publication-title: Proceeding of the ACM CCS Workshop on Rapid Malcode – volume: 18 start-page: 359 year: 2008 end-page: 369 ident: b0095 article-title: Thresholds for virus spread on network publication-title: Ann. Appl. Prob – volume: 141 start-page: 94 year: 1933 end-page: 122 ident: b0065 article-title: Contributions of mathematical theory to epidemics publication-title: Proc. R. Soc. Lon. Ser. A – volume: 104 start-page: 235 year: 1986 end-page: 259 ident: b0215 article-title: Some applications of Hausdorff dimension inequalities for ordinary differential equations publication-title: Proc. R. Soc. Edinburgh Sec. A – volume: 115 start-page: 700 year: 1927 end-page: 721 ident: b0055 article-title: Contributions of mathematical theory to epidemics publication-title: Proc. R. Soc. Lon. Ser. A – volume: 99 start-page: 392 year: 1974 end-page: 402 ident: b0180 article-title: Additive compound matrices and inequality for eigenvalues of stochastic matrices publication-title: Czechoslovak Math. J – volume: 27 start-page: 1070 year: 1996 end-page: 1083 ident: b0205 article-title: A geometric approach to global-stability problems publication-title: SIAM J. Math. Anal – volume: 3 start-page: 261 year: 1983 ident: 10.1016/j.amc.2011.03.041_b0225 article-title: The C1 closing lemma including Hamiltonians publication-title: Ergodic Theory Dyn. Systems doi: 10.1017/S0143385700001978 – volume: 66 start-page: 035101-1 year: 2002 ident: 10.1016/j.amc.2011.03.041_b0090 article-title: Email networks and the spread of computer virus publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.66.035101 – ident: 10.1016/j.amc.2011.03.041_b0195 – volume: 27 start-page: 1070 year: 1996 ident: 10.1016/j.amc.2011.03.041_b0205 article-title: A geometric approach to global-stability problems publication-title: SIAM J. Math. Anal doi: 10.1137/S0036141094266449 – volume: 18 start-page: 359 issue: 2 year: 2008 ident: 10.1016/j.amc.2011.03.041_b0095 article-title: Thresholds for virus spread on network publication-title: Ann. Appl. Prob doi: 10.1214/07-AAP470 – volume: 2 start-page: 295 issue: 4 year: 2005 ident: 10.1016/j.amc.2011.03.041_b0080 article-title: Network and epidemic models publication-title: J. Roy. Soc. Interf doi: 10.1098/rsif.2005.0051 – year: 2003 ident: 10.1016/j.amc.2011.03.041_b0140 article-title: Internet quarantine: requirements for containing self-propagating code – volume: 20 start-page: 857 year: 1990 ident: 10.1016/j.amc.2011.03.041_b0185 article-title: Compound matrices and ordinary differential equations publication-title: Rocky Mountain J. Math doi: 10.1216/rmjm/1181073047 – volume: 62 start-page: 58 issue: 1 year: 2001 ident: 10.1016/j.amc.2011.03.041_b0210 article-title: Global dynamics of an SEIR epidemic model with vertical transmission publication-title: SIAM J. Appl. Math doi: 10.1137/S0036139999359860 – year: 2006 ident: 10.1016/j.amc.2011.03.041_b0145 article-title: Effectiveness of quarantine in worm epidemic – volume: 96 start-page: 425 year: 1986 ident: 10.1016/j.amc.2011.03.041_b0160 article-title: Persistence in dynamical systems publication-title: Proc. Amer. Math. Soc doi: 10.1090/S0002-9939-1986-0822433-4 – volume: 187 start-page: 929 issue: 2 year: 2007 ident: 10.1016/j.amc.2011.03.041_b0010 article-title: Mathematical models on computer viruses publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2006.09.062 – volume: 141 start-page: 94 year: 1933 ident: 10.1016/j.amc.2011.03.041_b0065 article-title: Contributions of mathematical theory to epidemics publication-title: Proc. R. Soc. Lon. Ser. A doi: 10.1098/rspa.1933.0106 – volume: 115 start-page: 700 year: 1927 ident: 10.1016/j.amc.2011.03.041_b0055 article-title: Contributions of mathematical theory to epidemics publication-title: Proc. R. Soc. Lon. Ser. A doi: 10.1098/rspa.1927.0118 – volume: 106 start-page: 27 year: 1994 ident: 10.1016/j.amc.2011.03.041_b0200 article-title: On Bendixson’s criterion publication-title: J. Differential Equations doi: 10.1006/jdeq.1993.1097 – volume: 38 start-page: 269 year: 2004 ident: 10.1016/j.amc.2011.03.041_b0115 article-title: Immunization and epidemic dynamics in complex networks publication-title: Eur. Phys. J. B doi: 10.1140/epjb/e2004-00119-8 – volume: 217 start-page: 2520 issue: 6 year: 2010 ident: 10.1016/j.amc.2011.03.041_b0245 article-title: Dynamical behavior of computer virus on internet publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2010.07.064 – ident: 10.1016/j.amc.2011.03.041_b0085 – ident: 10.1016/j.amc.2011.03.041_b0045 doi: 10.1109/RISP.1994.296580 – volume: 11 start-page: 443 year: 1991 ident: 10.1016/j.amc.2011.03.041_b0230 article-title: Systems of differential equations that are competitive or cooperative. VI: A local Cr closing lemma for 3-dimensional systems publication-title: Ergodic Theory Dyn. Systems doi: 10.1017/S014338570000626X – ident: 10.1016/j.amc.2011.03.041_b0035 doi: 10.1155/2008/940526 – volume: Vol. 3733 year: 2005 ident: 10.1016/j.amc.2011.03.041_b0025 article-title: Keeping viruses under control – ident: 10.1016/j.amc.2011.03.041_b0155 – volume: 48 start-page: 119 issue: 1 year: 2006 ident: 10.1016/j.amc.2011.03.041_b0105 article-title: SEIR epidemic model with delay publication-title: J. Aust. Math. Soc. Ser. B Appl. Math. doi: 10.1017/S144618110000345X – volume: 89 start-page: 956 year: 1967 ident: 10.1016/j.amc.2011.03.041_b0220 article-title: The closing lemma publication-title: Amer. J. Math doi: 10.2307/2373413 – volume: 34 start-page: 710 issue: 3 year: 2010 ident: 10.1016/j.amc.2011.03.041_b0150 article-title: SEIQRS model for the transmission of malicious objects in computer network publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2009.06.011 – volume: 64 start-page: 1 issue: 066112 year: 2001 ident: 10.1016/j.amc.2011.03.041_b0125 article-title: Infection dynamics on scale-free networks publication-title: Phys. Rev. E – volume: 13 start-page: 961 issue: 5 year: 2005 ident: 10.1016/j.amc.2011.03.041_b0070 article-title: The monitoring and early detection of internet worms publication-title: IEEE/ACM Trans. Network doi: 10.1109/TNET.2005.857113 – volume: 99 start-page: 392 year: 1974 ident: 10.1016/j.amc.2011.03.041_b0180 article-title: Additive compound matrices and inequality for eigenvalues of stochastic matrices publication-title: Czechoslovak Math. J doi: 10.21136/CMJ.1974.101253 – volume: 104 start-page: 235 year: 1986 ident: 10.1016/j.amc.2011.03.041_b0215 article-title: Some applications of Hausdorff dimension inequalities for ordinary differential equations publication-title: Proc. R. Soc. Edinburgh Sec. A doi: 10.1017/S030821050001920X – volume: 190 start-page: 1207 issue: 2 year: 2007 ident: 10.1016/j.amc.2011.03.041_b0015 article-title: Fixed period of temporary immunity after run of anti-malicious software on computer nodes publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2007.02.004 – volume: 12 start-page: 242 issue: 4 year: 2007 ident: 10.1016/j.amc.2011.03.041_b0020 article-title: Dealing with software viruses: a biological paradigm publication-title: Inform. Secur. Tech. Rep doi: 10.1016/j.istr.2007.11.002 – volume: 1 start-page: 31 issue: 1 year: 2005 ident: 10.1016/j.amc.2011.03.041_b0040 article-title: Epidemiological models applied to virus in computer network publication-title: J. Comput. Sci doi: 10.3844/jcssp.2005.31.34 – volume: 160 start-page: 191 year: 1999 ident: 10.1016/j.amc.2011.03.041_b0175 article-title: Global dynamics of an SEIR model with varying total population size publication-title: Math. Biosci. doi: 10.1016/S0025-5564(99)00030-9 – volume: Vol. 3280 start-page: 667 year: 2004 ident: 10.1016/j.amc.2011.03.041_b0030 article-title: Biological metaphors for agent behavior – year: 1995 ident: 10.1016/j.amc.2011.03.041_b0110 article-title: A biologically inspired immune system for computers publication-title: Proc. Int. Joint Conf. Artif. Int. – year: 2002 ident: 10.1016/j.amc.2011.03.041_b0120 – start-page: 51 year: 2003 ident: 10.1016/j.amc.2011.03.041_b0135 article-title: Worm propagation modeling and analysis under dynamic quarantine defense – volume: 6 start-page: 583 year: 1994 ident: 10.1016/j.amc.2011.03.041_b0165 article-title: Uniform persistence and flows near a closed positively invariant set publication-title: J. Dyn. Differential Equations doi: 10.1007/BF02218848 – volume: 45 start-page: 432 year: 1974 ident: 10.1016/j.amc.2011.03.041_b0190 article-title: Logarithmic norms and projections applied to linear differential systems publication-title: J. Math. Anal. Appl doi: 10.1016/0022-247X(74)90084-5 – start-page: 31 year: 1991 ident: 10.1016/j.amc.2011.03.041_b0170 article-title: A brief survey of persistence in dynamical systems – volume: 138 start-page: 55 year: 1932 ident: 10.1016/j.amc.2011.03.041_b0060 article-title: Contributions of mathematical theory to epidemics publication-title: Proc. R. Soc. Lon. Ser. A doi: 10.1098/rspa.1932.0171 – volume: 188 start-page: 1476 issue: 2 year: 2007 ident: 10.1016/j.amc.2011.03.041_b0005 article-title: SEIRS epidemic model with delay for transmission of malicious objects in computer network publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2006.11.012 – volume: 213 start-page: 355 issue: 2 year: 2009 ident: 10.1016/j.amc.2011.03.041_b0240 article-title: A modified epidemiological model for computer viruses publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2009.03.023 – year: 2005 ident: 10.1016/j.amc.2011.03.041_b0130 article-title: The effectiveness of vaccinations on the spread of email-borne computer virus – start-page: 20 year: 1993 ident: 10.1016/j.amc.2011.03.041_b0075 article-title: Computers and epidemiology publication-title: IEEE Spectrum doi: 10.1109/6.275061 – start-page: 61 year: 2003 ident: 10.1016/j.amc.2011.03.041_b0050 article-title: Modeling the effect of timing parameters on virus propagation – start-page: 981 year: 2005 ident: 10.1016/j.amc.2011.03.041_b0100 article-title: Modeling virus propagation in peer-to-peer networks publication-title: IEEE Int. Conf. Inform. Commun. Signal Process. – volume: 206 start-page: 357 issue: 1 year: 2008 ident: 10.1016/j.amc.2011.03.041_b0235 article-title: Network virus epidemic model with the point – to – group information propagation publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2008.09.025
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Snippet	An e-epidemic SEIRS model for the transmission of worms in computer network through vertical transmission is formulated. It has been observed that if the basic...
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SubjectTerms	Computer network Computer networks Computer simulation Computer worms Dynamic models Endemic equilibrium Epidemic model Exact sciences and technology Global stability Mathematical analysis Mathematical models Mathematics Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Reproduction Sciences and techniques of general use Vertical transmission Worms
Title	Dynamic model of worms with vertical transmission in computer network
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