Fuzzy VEISV Epidemic Propagation Modeling for Network Worm Attack

An epidemic vulnerable—exposed—infectious—secured—vulnerable (VEISV) model for the fuzzy propagation of worms in computer network is formulated. In this paper, the comparison between classical basic reproduction number and fuzzy basic reproduction number

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Abstract An epidemic vulnerable—exposed—infectious—secured—vulnerable (VEISV) model for the fuzzy propagation of worms in computer network is formulated. In this paper, the comparison between classical basic reproduction number and fuzzy basic reproduction number is analyzed. Epidemic control strategies of worms in the computer network—low, medium, and high—are analyzed. Numerical illustration is provided to simulate and solve the set of equations. Keywords Epidemic threshold propagation

 Reproduction number  Fuzzy logic  Worm

1 Introduction Recent myriad research contributions in Internet technology are considered to secure the worm attacks and to analyze the dynamics of worms in network. To study the dynamics of worms in network, a mathematical model is to be developed to analyze the propagation of worms. Worms behave like infectious diseases and are epidemic in nature. The propagation of worms throughout a network can be studied by using epidemiological models for disease propagation [1–4]. Using Kermack and McKendrick SIR classical epidemic model [5–7], dynamical models for malicious object propagation were proposed, providing estimations for temporal evolution of nodes depending on network parameters considering topological

M. Senthil Kumar (&)  C. Veeramani Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore, Tamil Nadu 641004, India e-mail: [email protected] C. Veeramani e-mail: [email protected]

G. S. S. Krishnan et al. (eds.), Computational Intelligence, Cyber Security and Computational Models, Advances in Intelligent Systems and Computing 246, DOI: 10.1007/978-81-322-1680-3_32,  Springer India 2014

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M. Senthil Kumar and C. Veeramani

aspects of the network [1–4]. The similarity between the spread of a biological virus and malicious worm propagation motivates the researchers to adopt an epidemic model to the network environment [8]. Recent research in epidemic models such as SIR [8–10], SIS [8], SEIR [1, 11–14], SIRS [15, 16], SEIQV [17], and vulnerable—exposed—infectious—secured—vulnerable (VEISV) [18] is proposed to study the worm propagation by developing different transaction states based on the behavior of the virus or the worm. In particular, epidemic systems in computer networks have strong nonlinearity and should be treated in a different way. The nonlinearity is due to the force of epidemic of an infectious agent. This intrinsically includes the fuzzy logic analysis. Fuzzy epidemic modeling for human infectious diseases has been studied in many research contributions [19–22]. Recently, Mishra and Pandey [23] proposed fuzzy epidemic model for the transmission of worms in computer network. This motivated us to consider the fuzzy epidemic model for VEISV propagation for network worm attack. Our model generalizes Mishra and Pandey [23] work.

2 Classical VEISV Epidemic Model Toutonji et al. [18] proposed VEISV epidemic model for security countermeasures that have been used to prevent and defend against worm attacks. Thus, they