Quarantine And Antidotal e - Epidemiological Model For Viruses In Computer Network

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Kaveri Kanchan Kumari

Abstract

An e-epidemic  SIQRAS (Susceptible, Infectious, Quarantined, Recovered, Antidotal, Susceptible) model for the transmission of malicious objects in computer network has been developed and its various parametric characteristics are analyzed. Malicious objects, free equilibrium point and endemic equilibrium points are discussed by Jacobian Matrix. Stability of the system has been shown by using Routh-Hurwitz. MATLAB are employed to solve and simulate the system of differential equations.

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How to Cite
Kumari, K. K. (2018). Quarantine And Antidotal e - Epidemiological Model For Viruses In Computer Network. Journal of Global Research in Mathematical Archives(JGRMA), 5(5), 25–32. Retrieved from https://jgrma.com/index.php/jgrma/article/view/464
Section
Research Paper

References

M.E.J.Newman, Stephanie Forrest, Justine Balthrop, Email networks and the spread of computer viruses, Phys. Rev. E,

(2002), pp. 035101-035104.]

R.M.Anderson, R.M.May Infectious Diseases of Humans, Dynamics and Control, Oxford University Press, Oxford (1992).

R.M.Anderson, R.M.May, Population biology of infectious diseases I, Nature, 180(1999), pp.361-367

Bimal K. Mishra, Dinesh Saini, Mathematical models on computer viruses, Appl. Math. Computer.

doi:10.1016/j.amc.2006.09..

B. K. Mishra and D. Saini, “Mathematical models on computer viruses,†Applied Mathematics and Computation, vol. 187, no.

, pp. 929–936, 2007.

B. K. Mishra and N. Jha, “Fixed period of temporary immunity after run of anti-malicious software on computer nodes,â€

Applied Mathematics and Computation, vol. 190, no. 2, pp. 1207–1212, 2007.

E.Gelenbe, Dealing with software viruses: a biological paradigm, Inform. Security Technical Rep. 12 (4) (2007) 242-250.

Erol Gelende, keeping viruses under control, in: Computer and Information Sciences – ISCIS 2005, 20th International

Symposium, vol. 3733, Lecture Notes in Computer Science, Springer, October 2005

Erol Gelenbe, Varol Kaptan, Yu Wang, Biological metaphors for agent behavior, in: Computer and Information Science –

ISCIS 2004, 19th International Symposium, vol. 3280, Lecture Notes in Computer Science, Springer-Verlag, October 2004,

pp.667-675.

J.R.C.Piqueira, F.B.Cesar, Dynamical models for computer virus propagation, Math.Prob.Eng.,doi:10.1155/2008/940526

J.R.C.Piqueira, B.F. Navarro, .H.A.Monteiro,Epidemiological Models applied to virus in computer networks, J.computer

science. 1(1)(2005) 31-34.

S.Forest, S.Hofmeyr, A.Somayaji,T.Longstaff, Self and Non-self discrimination in a computer,in: proceedings of IEEE

Symposium on Computer Security and Privacy, 1994 pp .202-212.

Y.Wang, C.X.Wang, Modeling the effects of timing parameters on virus propagation, in:2003 ACM Workshop on Rapid

Malcode, ACM,Oct.,’2003,pp.61-66.

W.O.Kermack, A.G.Makendrick, contribution of mathematical theory to epidemics. ,Proc. Royal Soc. London –Series A 115

(1927)700-721.

W.O.Kermack, A.G.Makendrick, contribution of mathematical theory to epidemics. ,Proc. Royal Soc. London –Series A 138

(1932)55-83.

W.O.Kermack, A.G.Makendrick, contribution of mathematical theory to epidemics. ,Proc. Royal Soc. London –Series A

(1933)94-122.

C.C.Zou, W.B.Gong, D.Towsley, L.X.Gao, The monitoring and early detection of Internet viruses, IEEE/ACM

Trans.Interwork.13 (15)(2005)961-974.

J.O.Kephart, S.R.White, D.M.Chess, Computers and epidemiology, IEEE Spectrum (1993) 20-26.

M.J.Keeling, K.T.D. Eames, Networks and epidemic models, J.Roy. Soc. Interf. 2(4) (2005) 295-307.

Ma. M. Williamson, J.Leill, an Epidemiological model of Virus Spread and Cleanup,

http://www.hpl.hp.com/techreports/.

W.T. Richard, J.C. Mark, Modeling virus propagation in peer-to-peer networks, in: IEEE International Conference on

Information, Communications and signal processing (ICICS 2005), pp. 981-985.

Ping Yan, Shengquang Liu, SEIR epidemic model with delay, J.Aust. Math. Soc. Series B-Applied Math. 48(1)(2006) 119-

M.E.J.Newman, S.Forrest, J.Balthrop, Email Networks and the spread of Computer Virus, Phys.Rev.E 66(2002) 035101-

-4.

Hethcote, H. W., Lewis, M. A. and Van Den Driessche, P., 1989, an epidemiological model with delay and a nonlinear

incidence rate, J. Math. Bio. 27, 49-64.

Hethcote, H. W., 2000, The mathematics of infectious diseases, SIAM Rev. ,42, 599-653.

J. O. Kephart, T. Hogg. B.A.Huberman, Dynamics of computational ecosystems, Physical in computer, in: Proceedings 40

(1) (1989)404-421.

C.C.Zou, W. Gong, D. Towsley, Worm propagation modeling and analysis under dynamic quarantine defense, in:

Proceedings of the ACM CCS Workshop on Rapid Malcode,ACM,2003,pp.51-60.

Jose Roberto C. Piqueira, Vanessa O. Araujo, A modified epidemiological model for computer viruses, Applied Mathematics

and Computation (2009), doi:10.1016/j.amc.2009,03,023.

J.R.C.Piqueira A.A.de Vasconcelos, C.E.C.J.Gabriel, V.O.Arauja, Dynamic models for computer viruses, Computers &

Security 27 (7-8)(2008)355-359