Stability and bifurcation analysis of a modified epidemic model for computer viruses
type: Item
instance of: scholarly article
title: Stability and bifurcation analysis of a modified epidemic model for computer viruses
zbMATH Open document ID: 1407.34104
DOI: 10.1155/2014/784684
author: Chuandong Li
author: Wenfeng Hu
author: Tingwen Huang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 68M11
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 7017253
Wikidata QID: Q59072162
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/784684
OpenAlex ID: W2029988578
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description: scientific article; zbMATH DE number 7017253