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A Quarantine Model for Malicious Objects in Computer Network

Aditya Kumar Singh, Bimal Kumar Mishra


With a view to protect computer network from malicious object, SEIQS (Susceptible, Exposed, Infectious,Quarantined and Susceptible) models for the transmission of malicious objects with simple mass action incidence and standard incidence rate in computer network are formulated. Threshold,equilibrium and their stability are discussed for both the incidence rate. Global stability and asymptotic stability of endemic equilibrium has been shown. Numerical methods have been used to solveand simulate the system of differential equations which will help us   to understand the attacking behavior of malicious object in computer network.


Computer Network, Malicious Objects, Simple Mass Action Incidence, Standard Incidence Rate.

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M. N. J. Newman, Stephanie Forrest, Justin Balthrop, Email network and the spread of computer viruses, Rev. E 66(2002) 035101-035104.

R.M. Anderson, R. M. May, Population biology of infection disease, Nature 180 (1999) 361-367.

R. M. Anderson, R. M. May, Infection Disease of humans; Dynamics and control, Oxford University Press, Oxford 1992.

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

Erol Gelenbe, Keeping viruses under control, in: Computer and Information science – ISCIS 2005, 20th International symposium, vol.3733,Lecture Notes in Computer Science, Springer, October 2005.

Erol Gelenbe, Varol Kapton, Yu Wang, Biological metaphor for agent behavior, in; Computer Science, Springer-verlog, October 2004, pp.667-675.

J. R. C. Piqueira, F.B. Cesar, Dynamical model for computer virus propagation, Math, Prob. Eng. ,doi: 10 1155/2008/940526.

J.R.C. Piqueira, B.F. Navarro, L.H.A. Monteiro, Epidemiological models applied to virus in computer networks, J. Comput.Sci.,1(1)(2005) 31-34.

S. Forest, S. Hofmeyr, A.Somayaji, T. Longstaff, Self-nonself discrimination in a computer, in :proceedings of IEEE, Symposium on computer security and privacy, 1994,pp.202-212.

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.

Bimal Kumar Mishra, D. K. Saini, SEIRS epidemic model with delay for transmission of malicious objects in computer network, Appl. Math Computation,188(2) (2007) 1476-1482.

Bimal Kumar Mishra, Dinesh Saini, Mathematical models on computer virus, Appl. Math. Computation, 187(2) (2007)929-936.

Z. Feng, H. R. Thieme, Recurrent outbreaks of childhood disease revisited: The impact of isolation, Math. Biosci, 128 (1995) 93.

Z. Feng, H. R. Thieme, Endemic models with arbitrarily distributed periods of infection , I:General theory, SIAM J. Appl. Math 61 (2000)803.

Z. Feng, H. R. Thieme, Endemic models with arbitrarily distributed periods of infection, II: Fast disease dynamics and permanent recovery,SIAM J. Appl. Math. 61 (2000) 983.

L. I. Wu, Z .Feng, Homoclinic bifurcation in an SIQR model for the childhood disease, J. Differ. Equation, 168 (2000) 150.

D Green Halgh, Holf bifurcation in epidemic models with a latent period and non permanent immunity, Math. Computer model, 25 (1997) 85-107.

H. W. Hethcote, H. W. Stech, P.van dan Driessche, Periodicity and Stability in endemic models: a survey, in : K. L. Cook(Ed.) Differential Equations and Applications in Ecology, Epidemics and Population problems, Academic Press, New York, 1981 PP. 65-85.

K. L. Cook, P.van den Drissche, Analysis of SEIRS epidemic model with two delays, J. Math. Bio, 35(1996) 240-260.

M. Y. L. J.R.Graff, L. C. Wang, J. Karsai, Global Dynamics of a SEIR model with a varying total population size, Math. Biosci, 160 (1999)191-213.

M .Y. Li, J.S Muldowney, Global Stability for the SEIR model in edidemiology, Math. Biosci, 125(1995) 155-164.

M. Y .Li ,L. Wang ,Global stability in some SEIR epidemic models ;C.C Chavez , S .Blower, P. Vanden Driessche , D. Kirscner, A.A Yakhdu (Eds), Mathematical approaches for emerging and reemerging in infectious diseases ;Models, method, Theory, Vol.126,Springer 2002,pp.295-312.

Y .Michel, H. Smith, L .Wang, Global dynamics of SEIR epidemic model with vertical transmission , SIAM journal of Applied Mathematics, 62(1) (2001) 58-69.

J .K. Hale, Ordinary differential equations, second ed., Krieger, Basel,1980.

H. Hethcote, Mzhein, L. Shengbing, Effects of quarantine in six epidemic models for the infectious diseases, Math. Biosci. 180(2002)141-160.

B. K. Mishra, N Jha, SEIQRS model for the transmission of malicious object in computer network, Applied Mathematical. Modeling, (2009),34(2010), 710-715 .

Bimal Kumar Mishra, Samir Kumar Pandey, Fuzzy epidemic model for the transmission of worms in Computer network, Nonlinear Analysis:Real World Applications, 11 (2010) 4335-4341.


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