Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses | Zendy

Chuandong Li | Zendy; Wenfeng Hu | Zendy; Tingwen Huang | Zendy

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

Author(s) -

Chuandong Li,

Wenfeng Hu,

Tingwen Huang

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/784684

Subject(s) - center manifold , hopf bifurcation , mathematics , stability (learning theory) , bifurcation , bifurcation theory , epidemic model , transcritical bifurcation , equilibrium point , saddle node bifurcation , bogdanov–takens bifurcation , pitchfork bifurcation , bifurcation diagram , sequence (biology) , mathematical analysis , computer science , differential equation , physics , nonlinear system , population , biology , genetics , demography , quantum mechanics , machine learning , sociology

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

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