Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network

Abstract

A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.

Analysis of a Delayed Internet Worm Propagation Model with Impulsive Quarantine Strategy

“…People use quarantine strategies widely in worm containment enlightened by this [10][11][12][13][14][15][16]. In addition, some scholars have done research on time delay [17][18][19].…”

“…In view of the comparison theorem in impulsive differential equations [18,19], there exists an integer 1 > 0 such that…”

Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagation

“…Therefore, it is urgent to analyze the spreading law and control of computer worms in order to lessen their potential threat. Based on a newfangled observation that the spread of worms among computers is closely similar to the transmission of the infectious disease among a population, many epidemic models, such as SIRS model [4], SEIR model [5], SEIRS [2,6,7] model, SEIS-V model [8], SEIQR model [9] and SEIRS-V model [10][11][12], have been employed to analyze and describe the spread of computer worms in the internet.…”

“…All the work about the delayed dynamical systems shows that time delays have important effect on the stability of the systems. Therefore, based on the defects in the model proposed by Wang et al [15] and inspired by the work about the delayed computer virus models in [3,5,6,18,[31][32][33][34], we investigate a delayed e-SEIARS model:…”