DISCRETIZATION FRACTIONAL-ORDER SEIR WORM PROPAGATION MODEL IN COMPUTER NETWORKS

DISCRETIZATION FRACTIONAL-ORDER SEIR WORM PROPAGATION MODEL IN COMPUTER NETWORKS

R. Janagaraj , G. Maria Jones , A. George Maria Selvam

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Abstract

This model focuses on the investigation of potential worm-attacking behaviour in networked computers. Using epidemic theory, a discrete fractional order SEIR (Susceptible-Exposed-Infectious-Recovered) model is developed to represent the dynamics of worms in computer networks. Following parameter analysis, some successful wormremoval tactics are recommended. The discretized fractional order SEIR model considers the fractional order 0 < ϕ < 1 and step denoted by h. The nodes S(ℓ),E(ℓ), I(ℓ),R(ℓ) represent the fraction of susceptible, exposed, infectious and recovered populations with time ℓ with non negative parameters A, σ, μ, ϵ, α, ρ, β. Theoretical research shows that the Reproduction Number (RN) threshold RN0 determines the dynamics of the propagation of worms. When RN0 ≤ 1 the worm-free equilibrium is globally asymptotically stable, while RN0 > 1, the worm-endemic equilibrium is globally asymptotically stable. The analytical findings are backed by a numerical investigation.

Keywords

Epidemic Model, fractional difference equation, computer networks, basic reproduction number, global stability, neimark-sacker bifurcation