International Journal of Computer Network and Information Security (IJCNIS)
IJCNIS Vol. 9, No. 2, 8 Feb. 2017
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Pre-quarantine Approach for Defense against Propagation of Malicious Objects in Networks
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Author(s)
ChukwuNonso H. Nwokoye
1,*
Godwin C. Ozoegwu
2
Virginia E. Ejiofor
1
Index Terms
Pre-quarantine, Epidemic model, Wireless sensor network, Malicious objects
Abstract
This paper revisits malicious object propagation in networks using epidemic theory in such a manner that it proposes the (Pre-quarantining) of nodes in networks. This is a concept that is known by experience to be a standard disease control procedure that involves screening and quarantining of immigrants to a population. As preliminary investigation we propose the Q-SEIRS model and the more advanced Q-SEIRS-V model for malicious objects’ spread in networks. This Pre-quarantine concept addresses and implements the “assume guilty till proven innocent” slogan of the cyber world by providing a mechanism for pre-screening, isolation and treatment for incoming infected nodes. The treated nodes from the pre-quarantine compartment are sent to the recovered compartment while the free nodes join the network population. The paper also derived the reproduction number, equilibria, as well as local stability of the proposed model. Numerical methods are employed to solve the system of equations and MATLAB is used to simulate the system so as to visualize the dynamical behavior of the models. It is seen that pre-screening/pre-quarantining improves the recovery rate in relative terms.
Cite This Paper
ChukwuNonso H. Nwokoye, Godwin C. Ozoegwu, Virginia E. Ejiofor, "Pre-quarantine Approach for Defense against Propagation of Malicious Objects in Networks", International Journal of Computer Network and Information Security(IJCNIS), Vol.9, No.2, pp.43-52, 2017. DOI:10.5815/ijcnis.2017.02.06
Reference
[1]P. J. Denning, Computers under attack, Addison-Wesley, Reading, Mass, 1990.
[2]K. Hwang, G. C. Fox, and J. J. Dongarra, Distributed and Cloud Computing: From Parallel Processing to the Internet of Things, Morgan Kaufmann, 2013.
[3]P. Szor, The Art of Computer Virus Research and Defense, Pearson Education, 2005.
[4]J. Stankovic, “When sensor and actuator networks cover the world,” ETRI Journal, vol. 30, pp. 627–633, October 2008.
[5]E. Lule and T. Bulega,"A scalable wireless sensor network (WSN) based architecture for fire disaster monitoring in the developing world", IJCNIS, vol.7, pp.40-49, January 2015. DOI: 10.5815/ijcnis.2015.02.05.
[6]B. K. Mishra and I. Tyagi, “Defending against malicious threats in wireless sensor network: A mathematical model,” I. J. Information Technology and Computer Science, vol 03, pp. 12-19, February 2014. DOI: 10.5815/ijitcs.2014.03.02.
[7]B. K. Mishra and N. Keshri, “Mathematical model on the transmission of worms in wireless sensor network,” Applied Mathematical Modelling, vol. 37, 2013, pp. 4103–4111, September 2013. http://dx.doi.org/10.1016/j.apm.2012.09.025
[8]V. C. Giruka, M. Singhal and J. S. Royalty, “Varanasi, Security in wireless sensor networks,” Wireless Communications Mob. Comput., vol. 8, pp. 1–24, September 2008. DOI: 10.1002/wcm.422
[9]B. K. Mishra and G. M. Ansari, “Differential Epidemic Model of Virus and Worms in Computer Network, International Journal of Network Security, vol.14, pp. 149-155, May 2012.
[10]W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society A, vol. 115, pp. 700–721, August 1927.
[11]W. O. Kermack and A. G. McKendrick, Contributions of mathematical theory to epidemics, III–Further studies of the problem of endemicity. Proceedings of the Royal Society of London, Series A, vol. 138. pp. 55-83, 1932.
[12]W. O. Kermack and A. G. McKendrick, “Contributions of mathematical theory to epidemics, II–The problem of endemicity,” Proceedings of the Royal Society of London, Series A, vol. 141, pp. 94-122. 1933.
[13]N. T. Bailey, The Mathematical Theory of Epidemics, London, Griffin, 1957.
[14]R. M. Anderson and R. M. May, Infectious Diseases of Human: Dynamics and Control. Oxford, Oxford Univ. Press, 1991.
[15]W. T. Richard and J.C. Mark. “Modelling virus propagation in peer-to-peer networks,” 5th International Conference on Information, Communications and Signal Processing, pp. 981-985, December 2005. DOI: 10.1109/ICICS.2005.1689197
[16]P. Yan and S. Liu, “SEIR epidemic model with delay” Journal of Australian Mathematical Society, Series B – Applied Mathematics, vol. 48, pp. 119-134, July 2006. DOI: 10.1017/S144618110000345X
[17]M. E. Newman, S. Forest and J. Balthrop, “Email networks and the spread of computer virus,” Physical Review E, vol. 66, pp. 3, July 2002. DOI: 10.1103/PhysRevE.66.035101
[18]B. K. Mishra and N. Jha, “Fixed period of temporary immunity after run of anti-malicious software on computer nodes,” Applied Mathematics and Computation, vol. 190, pp. 1207-1212, July 2007. DOI: 10.1016/j.amc.2007.02.004
[19]H. Yuan and G. Chen, “Network virus epidemic model with point-to-group information propagation” Applied Mathematics and Computation, vol. 206, pp. 357–367, December 2008. DOI: 10.1016/j.amc.2008.09.025
[20]M. A. Safi, M. Imram and A. B. Gumel, “Threshold dynamics of a non-autonomous SEIRS model with quarantine and isolation,” Theory in Biosciences, vol. 131, pp. 19-30, January 2012. DOI: 10.1007/s12064-011-0148-6
[21]J. Zhang and Z. Ma., “Global dynamics of an SEIR epidemic model with saturating contact rate,” Mathematical Biosciences, vol. 185, pp. 15-32, September 2003. DOI: 10.1016/S0025-5564(03)00087-7
[22]Korobeinikov A., “Global properties of SIR and SEIR epidemic model with multiple parallel infectious stages,” Bulletin of Mathematical Biology, vol. 71, pp. 75-83, January 2009. DOI: 10.1007/s11538-008-9352-z
[23]M. Y. Li, H. L. Smith and L Wang, “Global dynamics of an SEIR epidemic model with vertical transmission,” SIAM Journal on Applied Mathematics, vol. 62, pp. 58-69, July 2006. DOI: 10.1137/S0036139999359860
[24]G. Li and Z. Jin, Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period. Chaos, Solitons and Fractals, vol. 25, pp. 1177-1184, September 2005. DOI: 10.1016/j.chaos.2004.11.062
[25]M. A. Safi and S. M. Garba, “Global stability analysis of SEIR model with Holling Type II incidence function,” J Math. Biol., vol. 2012, September 2012. DOI: 10.1155/2012/826052
[26]L. I. Wu and Z. Feng, “Homoclinic bifurcation in an SIQR model for childhood disease,” J. Diff. Eqn., vol. 168, pp. 150-167, November 2000. DOI: 10.1006/jdeq.2000.3882
[27]Z. Feng and H. R. Thieme, “Recurrent outbreaks of childhood disease revisited: the impact of isolation,” Math. Biosci., vol. 128, pp. 93-130, August 1995. DOI: 10.1016/0025-5564(94)00069-C
[28]Z. Feng and H.R. Thieme, Endemic models with arbitrarily distributed periods of infection, I: General theory,” SIAM J. Appl. Mathematics, vol. 61, pp. 803-833, July 2006. DOI:10.1137/S0036139998347834
[29]Z. Feng and H. R. Thieme, “Endemic models with arbitrarily distributed periods of infection, II: Fast disease dynamics and permanent recovery,” SIAM J. Applied Mathematics, vol. 61, pp. 983–1012, July 2006. DOI:10.1137/S0036139998347846
[30]H. Hethcote, M. Zhein and L. Shengbing, “Effects of quarantine in six endemic models for infectious diseases,” Math. Biosci., vol. 180, pp. 141–160, December 2002. DOI: 10.1016/S0025-5564(02)00111-6
[31]C. C. Zou, W. B. Gong and D. Towsley, “Worm propagation modeling and analysis under dynamic quarantine defense,” Proceedings of the 2003 ACM Workshop on Rapid Malcode (WORM 2003), pp. 51–60, October 2003. DOI: 10.1145/948187.948197
[32]O. Toutonji, S. M. Yoo, “Passive benign worm propagation modeling with dynamic quarantine defense,” KSII Trans Internet Inf Syst; vol. 3, pp. 96–107, February 2009. DOI: 10.3837/tiis.2009.01.005
[33]F. W. Wang, Y. K. Zhang, C. G. Wang, J. F. Ma, S. J. Moon, “Stability analysis of a SEIQV epidemic model for rapid spreading worms,” Computer & Security, vol. 29, pp. 410–418, 2010.
[34]Y. Yao, L. Guo, H. Guo, G. Yua, F-x. Gao and X-j. Tong, “Pulse quarantine strategy of internet worm propagation: modeling and analysis,” Computers and Electrical Engineering, vol. 38, pp. 1047–1061, September 2012. DOI:10.1016/j.compeleceng.2011.07.009
[35]B. K. Mishra and N. Jha, “SEIQRS model for the transmission of malicious objects in computer network,” Applied Mathematical Modelling, vol. 34, pp. 710–715, March 2010. DOI: 10.1016/j.apm.2009.06.011
[36]A. S. K. Pathan, H. Lee and C. S. Hong, “Security in wireless sensor networks: issues and challenges,” The 8th International conference of Advanced Communication Technology (ICACT) 2006, February 2006. DOI: 10.1109/ICACT.2006.206151
[37]P. Driessche, J. Watmough. “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29-48, December 2002.
[38]J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields, vol. 42. Springer Science & Business Media, New York, 2013.
[39]J. A. P. Heesterbeck and J. A. J. Metz, “The saturating contact rate in marriage and epidemic models,” Journal of Math Bio, vol. 31, May 1993. DOI:10.1007/BF00173891
[40]M. Kumar, B. K. Mishra and N. Anwar, “E-epidemic model on highly infectious nodes in the computer network,” International Journal of Computer Science & Engineering Technology, vol. 4, pp. 2229–3345, September 2013.
[41]B. K. Mishra and G. M. Ansari, “Differential epidemic model of virus and worms in computer network,” International Journal of Network Security, vol. 14, pp. 149-155, January 2012.
[42]B. K. Mishra and S. K. Pandey, “Dynamic model of worm propagation in computer network, Appl. Math. Modell., vol. 38, pp. 2173-2179, April 2014. DOI: 10.1016/j.apm.2013.10.046
[43]B. K. Mishra, S. K. Pandey, “Dynamic model Of Worms with Vertical Transmission in Computer Network,” Applied Mathematics and Computation, vol. 217, pp. 8438–8446. March 2011. DOI:10.1016/j.amc.2011.03.041.
[44]B. K. Mishra and A. K. Singh, “SIjRS E-epidemic model with multiple groups of infection in computer network,” International Journal of Nonlinear Science, vol. 13, pp. 357-362, February 2012.
[45]B. K. Mishra and N. Jha, “Fixed period of temporary immunity after run of anti-malicious software on computer nodes, Applied Mathematics and Computation, vol. 190, pp. 1207–1212, July 2007. DOI:10.1016/j.amc.2007.02.004
[46]B. K. Mishra and A. Prajapati, “Spread of malicious objects in computer network: A fuzzy approach,” Appl. Appl. Math., vol. 8, pp. 684 – 700, December 2013.
[47]K. Haldar, B. K. Mishra, “A mathematical model for a distributed attack on targeted resources in a computer network,” Commun Nonlinear Sci Numer Simulat, vol. 19, pp. 3149-3160, September 2014. DOI: 10.1016/j.cnsns.2014.01.028.
[48]K. Haldar, N. Narayan and B. K. Mishra, "A mathematical model on selfishness and malicious behavior isn trust based cooperative wireless networks", IJCNIS, vol. 7, pp.15-22, September 2015. DOI: 10.5815/ijcnis.2015.10.02