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Global Stability of Worm Propagation Model with Nonlinear Incidence Rate in Computer Network

In this paper, an e-epidemic SV EIS model describing the transmission of worms with nonlinear incidence rate through horizontal transmission is formulated in computer network. The existence of two equilibrium points: worm-free and endemic equilibria have been investigated. The stability analyses are determined by the basic reproduction number. It has been observed that if the basic reproduction number, R0 = σβ(μ+ θ)Λ η2(μ+ γ)(Λ(μ+ θ) + η1μc) < 1, the system is globally asymptotically stable and the infected nodes get vanish at worm-free equilibrium state; worms fade out from the network. However, if R0 > 1, the infected node exists; worm persists in the network at an endemic equilibrium state and is globally stable with some conditions. Further, the transcritical bifurcation at R0 = 1, has obtained using the center manifold theorem. The effect of vaccination and non-linear transmission rate on the dynamics of the model system has been observed. The dynamical behavior of the susceptible, exposed and infected nodes with real parametric values is examined. We also observe that the critical vaccination rate is required to eradicate the worm. Our results illustrate several administrative and executive insights.