INFORMATION CHANGE THE WORLD

International Journal of Computer Network and Information Security(IJCNIS)

ISSN: 2074-9090 (Print), ISSN: 2074-9104 (Online)

Published By: MECS Press

IJCNIS Vol.7, No.10, Sep. 2015

A Mathematical Model on Selfishness and Malicious Behavior in Trust based Cooperative Wireless Networks

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Author(s)

Kaushik Haldar, Nitesh Narayan, Bimal K. Mishra

Index Terms

Trust;ad hoc network;Malicious behavior;Selfishness;Epidemic model;Basic reproduction number;Endemic equilibrium

Abstract

Developing mathematical models for reliable approximation of epidemic spread on a network is a challenging task, which becomes even more difficult when a wireless network is considered, because there are a number of inherent physical properties and processes which are apparently invisible. The aim of this paper is to explore the impact of several abstract features including trust, selfishness and collaborative behavior on the course of a network epidemic, especially when considered in the context of a wireless network. A five-component differential epidemic model has been proposed in this work. The model also includes a latency period, with a possibility of switching epidemic behavior. Bilinear incidence has been considered for the epidemic contacts. An analysis of the long term behavior of the system reveals the possibility of an endemic equilibrium point, in addition to an infection-free equilibrium. The paper characterizes the endemic equilibrium in terms of its existence conditions. The system is also seen to have an epidemic threshold which marks a well-defined boundary between the two long-term epidemic states. An expression for this threshold is derived and stability conditions for the equilibrium points are also established in terms of this threshold. Numerical simulations have further been used to show the behavior of the system using four different experimental set-ups. The paper concludes with some interesting results which can help in establishing an interface between epidemic spread and collaborative behavior in wireless networks. 

Cite This Paper

Kaushik Haldar, Nitesh Narayan, Bimal K. Mishra,"A Mathematical Model on Selfishness and Malicious Behavior in Trust based Cooperative Wireless Networks", IJCNIS, vol.7, no.10, pp.15-22, 2015.DOI: 10.5815/ijcnis.2015.10.02

Reference

[1]J. Broch, D. A. Maltz, D. B. Johnson, Y. C. Hu, and J. Jetcheva, "A performance comparison of multi-hop wireless ad hoc network routing protocols," Proc. of the 4th Annual ACM/IEEE Int. Conf. on Mobile Comput. and Netw., pp. 85-97, 1998.

[2]S. Corson, and J. Macker, "Mobile Ad Hoc Networking (MANET): Routing Protocol Performance Issues and Evaluation Considerations," RFC 2501, 1999, Available at https://tools.ietf.org/html/rfc2501.

[3]K. S. Cook (editor), "Trust in Society," vol. 2, Russell Sage Foundation Series on Trust, New York, 2003. 

[4]L. Buttyán, and J. P. Hubaux, "Security and Cooperation in Wireless Networks: Thwarting Malicious and Selfish Behavior in the Age of Ubiquitous Computing," Cambridge University Press, 2008.

[5]M. Blaze, J. Feigenbaum, and J. Lacy, "Decentralized Trust Management,", Proc. IEEE Symp. on Secur. and Privacy, pp. 164 – 173, 1996.

[6]J. H. Cho, A. Swami, and I. R. Chen, "A Survey on Trust Management for Mobile Ad Hoc Networks," IEEE Commun. Surveys & Tutorials, vol. 13, no. 4, 2011.

[7]S. Ruhomaa, and L. Kutvonen, "Trust Management Survey," P. Herrmann et al. (Eds.), iTrust, Lecture Notes in Computer Science, vol. 3477, pp. 77-92, 2005.

[8]E. Aivaloglou, S. Gritxalis, and C. Skianis, "Trust Establishment in Ad Hoc and Sensor Networks," Proc. 1st Int'l Workshop on Critical Info. Infrastructure Secu., Lecture Notes in Computer Science, vol. 4347, pp. 179-192, Samos, Greece, Springer, 2006.

[9]J. M. Heffernan, R. J. Smith, and L. M. Wahl, "Perspectives on the basic reproductive ratio," Jour. of Roy. Soc. Interface, vol. 2, pp. 281–293, 2005.

[10]O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, "On the definition and computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations," Jour. Math. Biol., vol. 28, pp. 365-382, 1990.

[11]H. Inaba, "Threshold and stability for an age-structured epidemic model," Jour. Math. Biol., vol. 28, pp. 411-434, 1990.

[12]O. Diekmann, and J. A. P. Heesterbeek, "Mathematical Epidemiology of Infectious Diseases", Wiley, New York, 2000.

[13]P. van den Driessche, and J. Watmough, "Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission", Math. Biosci., vol. 180, pp. 29-48, 2002.

[14]C. P. Simon and J. A. Jacquez, "Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations", SIAM, J. Appl., vol. 52, pp. 541-576, 1992.

[15]J. M. Hyman, and Jia Li, "An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations", Math. Biosci., vol. 167, pp. 65-86, 2000.