Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses Academic Article

abstract

• 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.

authors

• Huang, Tingwen

published proceedings

• MATHEMATICAL PROBLEMS IN ENGINEERING

author list (cited authors)

• Li, C., Hu, W., & Huang, T.

citation count

• 5

complete list of authors

• Li, Chuandong||Hu, Wenfeng||Huang, Tingwen

publication date

• January 2014

publisher

• Hindawi  Publisher

published in

• Mathematical Problems in Engineering  Journal

Digital Object Identifier (DOI)

• 10.1155/2014/784684

URI

• https://hdl.handle.net/1969.1/178404

start page

• 1

end page

• 14

volume

• 2014

URL

• http://dx.doi.org/10.1155/2014/784684