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Modeling and analysis of the effect of network eigenvalue on viral spread

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Abstract

This paper aims to study the effect of network eigenvalue on the spread of computer virus. To this end, a node-based propagation model, which incorporates the impact of external computers, is proposed. A dynamical analysis of the model shows that the network eigenvalue plays a key role in controlling viral spread. Specifically, the global stability of virus-free equilibrium and the global attractivity of viral equilibrium depend on the value of the maximum eigenvalue of the propagation network. This result reveals that computer virus would tend to extinction or persist depending on network eigenvalue. Finally, some numerical examples are given to illustrate the main results.

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Acknowledgments

The author is grateful to the two anonymous reviewers and the editor for their valuable comments and suggestions. This work is supported by Natural Science Foundation of China (Grant Nos. 61572006 and 61503307), Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant Nos. KJ1500415 and KJ1500904), and Doctoral Scientific Research Foundation of Chongqing University of Posts and Telecommunications (Grant No. A2015-02).

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  1. School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Chenquan Gan

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  1. Chenquan Gan
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Gan, C. Modeling and analysis of the effect of network eigenvalue on viral spread. Nonlinear Dyn 84, 1727–1733 (2016). https://doi.org/10.1007/s11071-016-2600-0

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  • DOI: https://doi.org/10.1007/s11071-016-2600-0

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